{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Fb2ICfK2_oAE"
      },
      "source": [
        "$\\theta$-method, when $\\theta=0$ is equivalent to explicit method and $\\theta=1$ is equivalent to implicit method\n",
        "$$\n",
        "∂_t u = \\nu Δu \\\\\n",
        "\\dfrac{u^{n+1}_i - u^n_i}{dt} = \\dfrac{\\nu}{dx^2} ( \\theta (u^{n+1}_{i+1} - 2u^{n+1}_i + u^{n+1}_{i-1}) + (1-\\theta) (u^{n}_{i+1} - 2u^{n}_i + u^{n}_{i-1})) \\\\\n",
        "\\text{let } \\sigma = \\dfrac{\\nu dt}{dx^2}\\\\\n",
        "u^{n+1}_{i} - \\sigma \\theta (u^{n+1}_{i+1} - 2u^{n+1}_i + u^{n+1}_{i-1}) = u^n_i + \\sigma (1-\\theta) (u^{n}_{i+1} - 2u^{n}_i + u^{n}_{i-1})\n",
        "$$\n",
        "\n",
        "$$\n",
        "\\mathrm{AU}=\\left[\\begin{array}{ccccc}\n",
        "1 & 0 & & & \\\\\n",
        "-\\sigma \\theta & 2\\sigma \\theta+1 & -\\sigma \\theta & & \\\\\n",
        "& \\ddots & \\ddots & \\ddots & \\\\\n",
        "& & -\\sigma \\theta & 2\\sigma \\theta+1 & -\\sigma \\theta \\\\\n",
        "& & & 0 & 1\n",
        "\\end{array}\\right]\\left[\\begin{array}{c}\n",
        "\\mathrm{u}_{1} \\\\\n",
        "\\mathrm{u}_{2} \\\\\n",
        "\\vdots \\\\\n",
        "\\mathrm{u}_{\\mathrm{J}-1} \\\\\n",
        "\\mathrm{u}_{\\mathrm{J}}\n",
        "\\end{array}\\right]\n",
        "$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7jP2BJ0i9kaB",
        "outputId": "cc6d8976-adcb-4535-80e5-7c36465a9ea3"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "diffusion_1D_theta (generic function with 1 method)"
            ]
          },
          "metadata": {},
          "execution_count": 1
        }
      ],
      "source": [
        "# the code below is modified from https://github.com/DanPSilva/Partial-Differential-Equations/blob/master/Diffusion1D_Equation.jl\n",
        "using PyPlot, LinearAlgebra, SparseArrays\n",
        "\n",
        "function diffusion_1D_theta(NX,;theta=1/2,sigma=0.2)\n",
        "    # Nx = 41 ; # try changing this number from 41 to 81 and Run All ... what happens?\n",
        "    dx = 2/(NX-1);\n",
        "    NT = 20 ;   # NT is the number of timesteps we want to calculate\n",
        "    nu = 0.3    # the value of viscosity\n",
        "    sigma = sigma # sigma is a parameter, we'll learn more about it later\n",
        "    dt = (sigma*(dx^2))/nu ; # dt is the amount of time each timestep covers (delta t)\n",
        "\n",
        "\n",
        "    u = ones(Float64,NX);    # function ones()\n",
        "    s = Int(floor(0.5/dx));\n",
        "    e = Int(floor(1/dx));\n",
        "    u[s:e] .= 2.0;\n",
        "    un = ones(Float64,NX); # initialize a temporary array\n",
        "   \n",
        "    A = diagm(ones(Float64,NX)); # initialize a matrix\n",
        "    for row in 2:NX-1\n",
        "        A[row,row-1] = -theta*nu*dt/dx^2\n",
        "        A[row,row] = 2*theta*nu*dt/dx^2 + 1\n",
        "        A[row,row+1] =  -theta*nu*dt/dx^2\n",
        "        # (u[i] - un[i])/dt = nu/(dx^2) * (theta*(u[i+1] - 2*u[i] + u[i-1]) + (1-theta)*(un[i+1] - 2*un[i] + un[i-1]));\n",
        "        # then we have:\n",
        "        # u[i] - nu*dt/(dx^2) * theta*(u[i+1] - 2*u[i] + u[i-1]) = un[i] + nu*dt/(dx^2)(1-theta)*(un[i+1] - 2*un[i] + un[i-1]);\n",
        "    end\n",
        "\n",
        "    B = diagm(ones(Float64,NX)); # initialize a matrix\n",
        "    for row in 2:NX-1\n",
        "        B[row,row-1] = (1-theta)*nu*dt/dx^2\n",
        "        B[row,row] = -2*(1-theta)*nu*dt/dx^2 + 1\n",
        "        B[row,row+1] =  (1-theta)*nu*dt/dx^2\n",
        "        # (u[i] - un[i])/dt = nu/(dx^2) * (theta*(u[i+1] - 2*u[i] + u[i-1]) + (1-theta)*(un[i+1] - 2*un[i] + un[i-1]));\n",
        "        # then we have:\n",
        "        # u[i] - nu*dt/(dx^2) * theta*(u[i+1] - 2*u[i] + u[i-1]) = un[i] + nu*dt/(dx^2)(1-theta)*(un[i+1] - 2*un[i] + un[i-1]);\n",
        "    end\n",
        "\n",
        "    for n in 1:NT          # loop for values of n from 0 to nt, so it will run nt times\n",
        "        un = copy(u)       # copy the existing values of u into un\n",
        "        u = A \\ (B*un)         # solve linear equation\n",
        "    end\n",
        "    plot(range(0, length = NX ,stop = 2),u);\n",
        "end"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# explicit method\n",
        "diffusion_1D_theta(81; theta=0)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 466
        },
        "id": "ADFZEMrCsXS3",
        "outputId": "f6663238-7fde-43ba-e7ff-761c11443f1c"
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
            ],
            "image/png": 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"
          },
          "metadata": {}
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1-element Vector{PyCall.PyObject}:\n",
              " PyObject <matplotlib.lines.Line2D object at 0x7fc3fa225f50>"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# implicit method\n",
        "diffusion_1D_theta(81; theta=1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 466
        },
        "id": "OUA3khLvsgRk",
        "outputId": "0d55db16-3b7c-4994-8814-04dfed145c27"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
            ],
            "image/png": 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"
          },
          "metadata": {}
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1-element Vector{PyCall.PyObject}:\n",
              " PyObject <matplotlib.lines.Line2D object at 0x7fc3f72dea10>"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 466
        },
        "id": "Qdx8o3nED2xX",
        "outputId": "b005d912-407d-4863-fc69-203e0aa03276"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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keH3Qw0NI/KHgIbHE3ZfFL6Ule3iyqXCNB+2ydEYGGknYsvSS3EspjIfH6swsho1yHQmJOxQ8JJaIKqoRueqG5rf5yR6ejFWlFa4PzxAjPA1FlP0HRWCEgMmkU5bg8e+0XH1c8fpgHx5C4g8FD4kl9oaWARBgYFV4eII7LTOldSwIXZYu0pIpKS0ZIqUlXh9MaRESfyh4SCwRJlSRsvDb0FT+j+A+PNXfGaDgaSgDdfbhyaQNq3mkfxrT/fpghIeQuEPBQ2KJO2URptNyxhHh0R9vmiartI4BpmlaEZ5A07KjW3ZwWrJUCZ/yJITEAwoeEkvcHp4wFTsZabP0K2MvV0yYtbuZ0mocxbIJsQxh2wSkUyE7LbsED/vwEBJ/KHhILPGmLILTG2lpWno5RFUXAAyVKjBN+j8agdzFOrjxoJTSSgf7sNxVfMUS15CQuEPBQ2KJJ6UVpkrLMUtLf7w7GjDECp+GIEfPShUTlRCdk7NpewCszodVqdiRI6a0CEkOFDwklogNrNXqsxKc3qjO0krVfj84IiRgWqsxuCfRu7sjq+6TK+10zSbl10IrTcuEJAYKHhJLCiV3Y7lgD086lZI6M9cjeLhZNgK3kPQToXLn5KDREnL0Trw+6OEhJP5Q8JBY4k5pVY3Gmg1QlKWn7JJmv2/8br8HIzyNwS0k/eZd2d2yU4EeHlk4MaVFSHKg4CGxxC14AL9v/LaHJ8zgSXc0QDbXkqOH+3n1HxXhFa26NZSjd5bgoWmZkNjTUMGzdu1afPSjH8WkSZNgGAYeeughx/2maWLp0qU4/vjj0draijlz5uC1115zHLNv3z586lOfQnt7O0aPHo0FCxbg0KFDjmNefPFFXHDBBWhpaUFXVxduvfXWRl4WiQDuKi1A/42/LHl4siG69Lo33oECBU8jcD+vfmkn23ieCvbw1B7HMIB8hhEeQpJCQwVPf38/ZsyYgeXLlyvvv/XWW3HXXXdhxYoVWL9+PUaOHInu7m4MDg5ax3zqU5/Cpk2bsHr1ajz88MNYu3Ytrr76auv+vr4+zJ07FyeddBI2bNiA2267DTfffDN+8IMfNPLSSJNj9+HJWLfpTK8ixZFOpexOy34pLXp4jgn1eHiK8sT7lP8EdNFjKSt5tujhIST+ZIIPOXI+9KEP4UMf+pDyPtM08Z3vfAc33ngjLr30UgDAv//7v6OzsxMPPfQQLr/8cvzpT3/CqlWr8Oyzz+Lv/u7vAADf/e538eEPfxjf+ta3MGnSJPz0pz9FoVDA3XffjVwuhzPPPBMbN27Et7/9bYcwIslC+D3klJaut46IBGTT4WZpeQQPU1oNwT2JPsz082qUrtZLSZfSksZQZDPBni1CSDwYNg/Ptm3b0NPTgzlz5li3dXR0YObMmVi3bh0AYN26dRg9erQldgBgzpw5SKVSWL9+vXXMhRdeiFwuZx3T3d2NLVu2YP/+/cfoakizITawfMZ+iesiPMrhoX59eFx+D05MbwzuCI/feAm7tUAq0Icll7ALccThoYTEn4ZGePzo6ekBAHR2djpu7+zstO7r6enBhAkTHPdnMhmMHTvWccyUKVM8jyHuGzNmjOf/HhoawtDQkPVzX1/fO7wa0mwIwZPLVNMWxbIZysMTZngoU1rHBreQDGNalqN0eg+P3aQwl2aEh5CkkMgqrWXLlqGjo8P609XVNdynRI4yBUXnXV2KwypplgyvdaW0GOFpCJ6ydN9REVKULu3v4RHROzn9FTSclBASfYZN8EycOBEAsHv3bsftu3fvtu6bOHEi9uzZ47i/VCph3759jmNUjyH/H25uuOEG9Pb2Wn927Njxzi+INBVF6xu/NBBU8y2+LG2AmRCjJSh4jg1e03JwSiubTlndsnUC1+n38X9tEELiw7AJnilTpmDixIlYs2aNdVtfXx/Wr1+PWbNmAQBmzZqFAwcOYMOGDdYxv/3tb1GpVDBz5kzrmLVr16JYLFrHrF69GqeddpoynQUA+Xwe7e3tjj8kXtgpLVvEaDdAycOTtaq0/PrwuBoPMjrQENxmcL9KqpJUpZUJ7LRsR/Rs0zI9PITEnYYKnkOHDmHjxo3YuHEjgKpReePGjdi+fTsMw8DixYvxjW98A7/85S/x0ksv4bOf/SwmTZqE+fPnAwDOOOMMXHLJJbjqqqvwzDPP4Pe//z0WLVqEyy+/HJMmTQIAfPKTn0Qul8OCBQuwadMm3H///bjzzjuxZMmSRl4aaXJElVY2bZeaa1Mc0jf+dEA0SH5sASM8jSFsp2XTNKXWAlLzSM0aWk0K0wY9PIQkiIaalv/4xz/ioosusn4WIuRzn/scVq5cieuvvx79/f24+uqrceDAAbz//e/HqlWr0NLSYv3OT3/6UyxatAgf/OAHkUql8LGPfQx33XWXdX9HRwcee+wxLFy4EOeeey7GjRuHpUuXsiQ94Tg9PP5pKsc3/oB0CKBoPEjB0xDcz6tOsMpLlQ0xD63kaDRZ8/BQ8BASexoqeGbPnq2dXwQAhmHglltuwS233KI9ZuzYsbjvvvt8/5+/+Zu/we9+97sjPk8SPxwenoDuyWWpTDktPB11CB73VG9ydAjr4ZFvT6ftifeBKS1JHDHCQ0j8SWSVFok/lodHitrofDkOE2sqeFq6x8PDCE9DcAtJXRRGXqtsSq60809pZdNSHx7O0iIk9lDwkFhiRXgyITwd8hwmqUuvLjrJKq1jg/t5DRKsQM20HBDRk/0+OXZaJiQxUPCQ2CGbWGXTctD0bNm0DPjMYvKYlrlZNoKw09LlDtqZlNx4MGC90yl6eAhJEBQ8JHbIQiWbTkkT0HURHnnUgC149I0Kq8e31iaxc5ZWYxBCUjzP+j5KdsTGMMJ4eOSUFj08hCQFCh4SO+TNK5dOBU7Plj08oiszoJ+9JTw8bS1Vzz9TWo1BPK/iedZFYcR6i8hOkIfHTmnJoyXo4SEk7lDwkNhRckR4jMBSc4eHR0pp6TwjYoNtb80CYEqrUQjBI55nnbFYFqwAQlflZV2T1Ss+RnVCSPSh4CGxQ0QCDMM9W8k/JZJJGUilDAjNo0uBicdhhKexCCEpnmfd+smCFUCgh8eenWZYnZYBfUSPEBIPKHhI7JB78FQ9Hf4DQcXxaStC4F/GXrRSWiLCQ8HTCOyUVi3CoxU8ticHgOXh0acwRQos5fBsMa1FSLyh4CGRYvvbh7Hwvufw4psHtMfIPXgAONIWKsTtYvMLmpjujfAwMtAIwnp45EnpAKTZaUERITvdCehHVwDAs2/sw6L7nsPuvsF6LoEQ0kRQ8JBI8dDGnfj1i3/Fz57Zrj2mWHZ/4xfdk/03QBEZCBpFYXl4hOBhlVZDEENZ28OmtDzrFzwsNiWVsftVaq18+g08/OJf8esX/1rvZRBCmgQKHhIp9vUXAAD9Q3qRUSjZPXiqf/tHbGQPj/x7+sZ1IsLDlFajKJYr1rpYKS2taVktcLUmdXF8yhkB9OvFc3ioBAA4cLgQ/iIIIU0FBQ+JFH0DRQD+IkP28AD2N/8gAZNxR4Q0G6AQVG15O6XlNzOO1I+8vuJ51s/Scqa0sgEeLDmlJf/t5+ERacve2uuPEBI9KHhIpBAbjt+EcndKK6gvi9y4rvp7/p4ft4cHAIZ8/B+kfmRf1KgAD4/twaquWzogJekuY7d78ejXULzeKHgIiS4UPCRSiA3Hb0J5wR3hCezL4vKABHzjd6e0gs6H1I+I8OQzqcB5V8KblXEJXK1gtY53pbR8ROsgBQ8hkYeCh0QKseH4GYXlOVpAiDJzabSE/Le+U2/19hG5tHUsjctHl6Ha89maS9sTzQM6ZQvTeVBn7XLZmdLKZoJNyyKCR8FDSHSh4CGRojeMh6ckJqWHq7oqWwKptgEGdGYWoyVymRRaav8HjctHF5HSasmkA1NOcudkIDglWdKY1P09PIzwEBJ1KHhIpLAFj/7buN2HR6Q4AiIELg+PldLSpURKdsqspTbY0s9TROpHPJ8t2VRgyqnoitgEeXiKUuNBIJyHxxY8pfAXQQhpKih4SGQYLJat1IJfRMXt4cmGbUTn7uMSkNKSBQ+bDx5dBi3Bkw6caC6ETdg+PO5Gk2HK0sX69g0ywkNIVKHgIZGhT0on+Jelq6t2AkcNWGXK4crYcxkD+SxTWo1ACIx8Nm2lJgOn3bvXL2A0SDrlFMS6TsumaVoerUKpwrUmJKJQ8JDIIPsnBn0qajx9eCwBEzw8VP47aMPMplNoyYgIDzfBo4kV4cmkAlNOugid3sPjbFsQ5OEplCuQ2yzRx0NINKHgIZFB3mgKpQoqISIwgG1mDTKxuj08OoFUcKS0RISHKa2jiTOl5Z9ysoeBuj084UzLQWXvgwXn7RQ8hEQTCh4SGdz+CV0peKHkjPCkA/rqeCMEQSkRr4dniGXpRxURwaualoM8PK6UVmDjwVobAncfHp3gca0tBQ8h0YSCh0QG90aji6q4PTxZS8B4jzdN005pWSmOgCqfkj2N3TYtU/AcTYYUER79LC1136VygOfHLmP3F1Tute09TMFDSBSh4CGRwb3R6ESG18OjT3HIaS53SkTfabm2YWYMtLJKqyGItW2VBU9Ap+W024MVlNJyRXh0pmX32jLCQ0g0oeAhkcHdAyVI8OQ8s7S8G6C8KdoeHn3jOtM0rdRHJpWyqrTYh+foMqAoS9fO0nI1jgycpVVxen5yAaZlT4SHgoeQSELBQyJD2JSWd5aWvkpLFjx2Ckyf4pCPZ0qrcdhl6akQER71LDR9WwF3CjPAw0PBQ0gsoOAhkcEjeDRGYeH18I6WUKS0yt4Ij+jPojpe3nSzGUMqS2dK62hil6WnpSoq/z5KdkqrerxpQlnJ5x4WGzRLy90CgYKHkGhCwUMigzfCU6eHR5nSsjezjMvEqkppycZZZ1k6IzxHE2uWluThKVdMXwHjTmkBatHqLmMPiiC517aPgoeQSELBQyKDe6MZ0lZpqWdp+aW00ikDhuGapaXYAOW0RyZlsCy9QYjonVyWDtgGZRk7ReXsnAz4r7lYZ3p4CEkGFDwkMoSN8OhmafmZluWogF8fHltMpWAYBhsPNghVWTqgFiVuE3JwhMfVtiBgOCkFDyHxgIKHRAax0YwZkQXg4+HxzNKqfYP38fBkHIJH7/mx02XVY2habgx2SivlFDwKUaJrHAmoe/G4y9iDU1rV28XrjoKHkGhCwUMig9hoJrS1AAAGCpqUlui0nHF6eFTT0t2bH2B3ZlY1KrQET+2xOUurMcim5XTKkHojKQSPa/irtJTKFJhnWnqQabl2LuJ1R8FDSDSh4CGRoFCqWL1ZJrTnAYTvw5P1SVHZm5/9Vsj6VGkVSs7jW3Ks0moEloen9vz69eIpuaJ0hmH4Gs/t46trGOzhqf6f4nVHwUNINKHgIZFA3mTGt9UEjy6lVXGntPyiAwoPj89oCdnDA1SneQNsPHi0GSjYER7Af6K5u3MyIDUf9PFhhU5p1V5nne3VCM9QqcKIHiERhIKHRAIheNpaMhgREFUpltSmZeW3fZfhVf6332ZJD09jkT08gByFUXl4VGuoj9K5o3phy9LHjcqjVsjH0nRCIggFD4kEQvB0tGatb/1DofvwhIkOyBEe/fHuCjC7LJ0praPJUMmu0gL8K6ncnZPlfyt9Wy7Pjz081D+l1ZpNo72FxmVCogoFD4kEfbLgCYiqWGmnjHuYpN7AKlf2iOPVm6XLw8PGgw1BbjwI+BuLrYiNYg2VZekVp+fH7uSsFq12iXwKHa0UPIREFQoeEgnkCE9rQEqr4DKlZkIYWNOKlJaqjL3krtJiSqshDEoiA/D38Lg9OfK//XoviUieeJ1o+/DUok2tuTQFDyERhoKHRAJZ8ORrYkPfh8eV0kr5pbQU/g8xysC38WDNw8NZWkedUrliiRLx/Pp5eMqqtKSPh8cSrSl3Sku9hrKBmoKHkOhCwUMiQe/RSGn5TD+XN8usT5VWQZfSKpVhmmoPSLliYs2fdmNff0F7fUliz8FBPL55j3IuFuAc1unx8PhU2smtBXQenkrFhPhvrSqtgOGk8uR2Ch5CogsFD4kEKsEzELJKyy4z13daTkv+j7RPRMj92KJPjGmqN2MAWP1KDxbc+0fc8tOVwrkAACAASURBVKtN2utLEl958CVcsfJZrHv9beX9spAV0TwrCqMyLauaR2pSWvJrQETy/KJHgDzXK412Ch5CIgsFD4kEYoNpb80GGoXdURjxt9rA6k1p+U5Ld1dp1VIu1fNRb5jb9x0GALy4s1d5f9J44c3q87Cj9ry4Eeuaz6SQ8vTKCZ6WDuhNy3LUzuq07BM9qp6PbaBmhIeQ6ELBQyLBOylLT6dsAeNOO7krdqr/1n/jd6fLsmnDGmWgE2Di3Le/fVgbRUgKvQNF7D04ZP1bxWDRWZIO+FdSFV0mdfnfbsEjC6Z0SA+PVaWVsVNafQMl5bGEkOaFgodEArWHR5PScnVDlsuV3RugyvCa9ilpdkePqhPT/T1F4txLFRN/eVsd1UgKr+89ZP1bL3icTQeBIA+Pyniu9vDIUTvxurCiRyWdh8cWYIzwEBJdKHhIJHD24QlZpSVMy5KY8Xg6FB6erI/nxx09AhAowHqlaMCfpQ0/ifx5b7/173oiPH5RmLKrzBzw8fDUfj9lwEqXBfXhESZqWfCw0zIh0YOCh0SCsFVapml6mgPKZlb39Gzh6cgqytKV09JLCsGT8fcUyRt70gXP1j11RHgysuARURi9adlRaadLaSkaTQZ7eNh4kJA4kBnuEyAkDLLgEZuYKqIiezTcpmXA21tHPJaq8aDfLK2ctLmGTWkBzg0/ifw5VErL2XQQCBgeWvb6sHRpybJiDIVf9Mg0Tet8WpnSIiTSMMJDmp5iuYLDteZvHQFVWvKmJTw80j7oifCom9aF78MDAHkheDSdevscEZ5+5TFJQRY8urSQSFXmFSktpYdHNR5E4+FRlbDnfMRUoVyx+vbkKXgIiTQUPKTpkTeXdimlNVSqeKquZMEjNknDMGxfTlldtZN2bJb6MnbbHyR7ePxTWvLG/vqeQ9oGhXGnWK5gu2TaDjYtK1JaPqblrMJ47hYxqiaF4t/liulpRSBHEeWU1kCxrB1FQQhpTih4SNMjNsa2fAbplOHYCN1TykUEwDDcaSp7U5Mpqzw8IVJa8obZGuApkjf2g0Mlqyw7afzl7X6HiAxKabUqU1r6Tsth1lvZd0kSr+7HFyXphlGNBLW1ZGAY/udPCGlOKHhI0yM3HQRskzBgzzkSyIZlw/CKGPeGpvTw+IyW8PPwDCk8RYcLZev/mNCWB5BcH8/WPdV0nnge+gZLymiXfx8e/TBQx2gJXeNBhd9Hjgy5Xx+ygdowDKRSBtryVesjBQ8h0YKChzQ9smEZqKacxIblLk0XVTy5tPOlrRsvoTaxiiothaej5N1cRUprQBHhEeeeTRs464QOAMmt1BLXfe5JYwBUoy+HhrwN/CzBk1F4eBRppJKiSistPDwegSuOlaJHKTnC40pplbwG6o4R9PEQEkUoeEjT0+cSPIC+901R4ecA5FLz4DLltCYaJN+WcZSl61NaslibNmEUgOQal4XgOXNSuyVI+wZVgkffeNC9JnIbAjlKlw2K8Eivj1TK0EYAVdEm9uIhJJpQ8JCmxx3hAfRG4YLCYwPoK6/KiqqdrMb/AahTWnmfxoNyOu6U8ULwJDTCU0vlTZswyh7CedgrGtSNB9WCVV6irGIArHeWljelJT++O4KkMlCzUouQaELBQ5oesSmqIzx6D49Mxuq1EmKWljg2dKdlfednWaydMmEkAHvjTxKmaVqRrVPGj0JHq94HoypL1000l39WtRZwi1YrQpdyvj50vXj8IjwUPIRECwoe0vRYomFE+JRWLuPa0HRVOyIdourDo0hpqfrw+DUedAieWoRnV+8g+hXelTiz5+AQDg2VkE4ZOPG4Eb6iQZ3SUvfhkSM4jrSkRsCoJqsDelO0qgkiBQ8h0YSChzQ9viktjWnZvaGlNSLG2gAVfXgqJlBxRwjE42dUHh6vQJL9R6NH5DBuVA4A8HrCfDwiqnXi2BHIZ/xnUilNy5p5V3LnbOdoCV2Ex+v3AfQeoQHFubRT8BASSSh4yLDzyq4+LH98qzKiAnjL0gF7AxoK6+ERG5qmL4uqLL16vzol4ixLTynPRT53scFPTaiPZ2vtekWUK1yER9V40G06l1JajtESOg+P13QuP747gjSkiDa1t/gLnsFiGXeteS2x7QcIaVYoeMiwMlgsY8G9z+K2R7dg1aYe5TF9g/VUaak9PFnNqAFVXxb5326Ts7LxYE6MlggWPEk1LosIj/Ax+Qmeodrz2Jqzn2Odh0duOujou5QOiOil3RGeWgrMbVou1e/heej5nfj26ldx9f/5o1bEE0KOPRQ8ZFj56frt+GvvIADg1Z6DymN6B6p+F1VKy937xo7AOF/a2lED1iwtuWldynO/QOnh8UlpeQVPzbicNMEjGZaBoAiPqg+PuopK1TlZ/tkbofOOEpEfX+/hCS94Ntdex6/v7ceDz+9UHkMIOfZQ8JBh49BQCd97fKv181aNCFD14clrq7SEx8b1DV6kOFwbWllVpSVHeDyzt7wRnrwQXwV9hEek40QvnqSlO/7sSmn5+WAGlGXpmk7Zuqo8jYfHmruV0pmWdWXpXtOyrg+PLGbv/M1rVsSKEDK8UPCQYeOep7bh7f6CtZn9eY/ayKs0LWuiKoWSzsOj7sOjGi2RShnWhHV3SsKuAvOOlqgnpfXGW4cTk+44NFSyonjT6vDw5OUqLU0VlcqDVf05oA+PJ6Wl9vAIQZ3PhI/wiPRdNm1g54EB/Gz9duVxhJBjCwUPGRYOHC7gB2tfBwAsnnMqAGDbW/3Kb+Ri/ECYxoMlRedkQK7S0nzj13Vm1lVpKcvSfRoP1oyuJ4xuRT6TQqFcwZv7BzzHx5HXaxGPcaPyVmuBUCmtEH14ShpPjs7DU9L04dENjK238WD/UAm7auJOvK7/38e34nAhWW0ICGlGYiV4li9fjpNPPhktLS2YOXMmnnnmmeE+JaLh39a+joNDJZw+sQ1fuHCqJAIOO46TRw+0t2Ssf7dqoiqqCAxgCxTv9Gy1p0O3Aao9PPoqLXc6LpUyElepZaezRlq3+Zel2wM7BboIjGpSOuAzPFQT4dGmtISBWiF4DhfKnuO3vVWNUo4blcNVF0zFiWNH4K1DBax8+g3PdRJCji2xETz3338/lixZgptuugnPPfccZsyYge7ubuzZs2e4T4242HNwEPf8fhsA4EvdpyGTTmHKOLWZV3yLHpXPOOdXaSaUa1NawrTsGS2hHjWgO17daVntJzJNU9k0McjHs+2tfryyq085SbwZqVRMvLyzF9vfPqy8X6QqT6ldN+A/gHNI0exP5+HRdU5O6zw8mghgUErLUZYuRRrd5y/WdOr4UchlUrj24ncBAFY88Wf27SFkmImN4Pn2t7+Nq666CldccQWmT5+OFStWYMSIEbj77ruH+9SIi+W/3YrBYgV/e+Jo/P3pEwDYm6FbBKj8O4A+pRU0WkJnQtY1otONJsipBI+rgmigWLbORz5/v0qt1/ceQvd31uLDd/0O7/3fa3DdAy/gVy/swoHDBc+xw8nbh4bw0PM7sfg/nsffffM3+Mh3n8KH7lyLv/Z603RiTYV/CXCmhdzCTlUKblVRldSmc09KKyCF6Z2lFX60RDploC2vHo3hNmf/PzNOwKmdo9A3WMIPaylcQsjwkAk+pPkpFArYsGEDbrjhBuu2VCqFOXPmYN26dcN2XqVyBbevfrWu3zkaX+pNKB4k6HEN8ZcBw7BvMqTbgeo34IFCGYPFMgZL1X+XKhWMzGUwKp/BqJbq320tGUweMwLnTTvO8q8AwI59h3HfM1UT55e6T7N6p1j9aVzGZVXTQcBvlpYuwqP25JQ1KQ7dxHRVFZhOfIlzT6cMjMzZG6bdi8dr0r7jN69ZUaq9B4fwn8+9if987k2kDOBvJo/GCaNbPc9zLpOqrkexgsFiGQO1f4su0crXQw2xrum0gZZMGi3ZFFqyabRm08hnUyiUKjg4WMKhoRIODhZxaKiEN/cP4KWdvZ7Xan+hjO/+div+9387y3G7X0qrVDFxuFDGyJqAKFfs6ecOD48m5aTrnGx7sNSeH51p2dOHR1GlBVRfjweHSp6UnPta0ykD1809DV/4Pxtw9++34XPnnYzxbXnr+N7DRfz+z29h14EB63k+VPu7v1BCNi3Wo/p3SzZtiW0TprUGYilMU1rvkO95502KGxuIcWz/OzLMZGrvh2H7/4ftfz6KvPXWWyiXy+js7HTc3tnZic2bN3uOHxoawtDQkPVzX19fQ86rYgLff+LPDXnsqJBJGTjnpDH4wKnjMfu08bj7qTdQLJt4/7RxOO+UcdZxIs2jS2mJYZMC3YRyVSdkwMfEGpDikCMEpmkqI0itkvgyTdMScXJ0Sm6KJwTP1j2HHMe/sqsPv3phFwDgoYXno3+ohCe27MGTr+7Fq7sPYeOOA9i44wCahTOOb8fs08bjA6eOR6Vi4pM/Wo8Hnt2Bqy+YipNrKcpSuYI33q4Ku2lSSqs1m0Y2baBYrqb9hOCRRWOrIsLjnaXln8LUzU5zH5+row8PUF3TnQcGvBGePd5rnTu9EzMmd+CFN3ux/PGt+IdzTsATW/biyVf34vnt+1E5Cl9yCIkCuUyKgudYs2zZMnzta19r+P+TMoAF759yVB6r3i9Cqm9OhubrlGmatW+GkL4x1qIDrg/jXEZ800yhtfaNM50yMFAo16IAJRwaKuLgYAkvvdmL19/qxzPb9uGZbftw26NbrMf5l27ni16X5tGmtDLqWVra0RIaE2tZUZYOyGXs9vHyv519eKqbYcWs/v+ihFk15R0Apo4fCcOoXtu+/gKOG1X9xn/7Y9Xn5yN/czzO7hoNADh/2jh8dR6w68AAnn1jHw4cLlrPs4i4FEoV69u/iNC0ZNKeKIa8/O51LZYrVoRoqGRHi/KZVC2alEVbLao0ZmQOM6eMRWd7i+MxPnDqeDz56l585zev4juX/y0AYMf+ARTLJlqyKUzqaJXOxUB7SxZv9xfQO1DEpNHV++RGkvlMsIdHF7FJa9a7qCljr6csHVBXapXKFcu0LKfvDMPAl7pPx6d/vB4rn37DY2A+tXMUph/fjraWrCNy15pNo1g2a9HUMgYL1aiqu/miHIV1R2f93vPe25SH1gW1G/HDnUo+5v//sP7vR4lx48YhnU5j9+7djtt3796NiRMneo6/4YYbsGTJEuvnvr4+dHV1HfXzyqRT+F8fmX7UHzdKbH/7MJ58tRql+P3WtzFQLGPeWfaGLpg6rrpB7D9cFQFjR1aHbKqaDgL2N253sz/h8chm3B4edeNBXVm6atiovNk6PTz2vweLkuDxScdNHtOKHfsGsHXPIRw3Ko8Nf9mHNZv3IJ0ysOTiU+Fm0uhWXHr2CZ7bm4l/mXsannx1L/7rhV24ZvY0nDaxzepJM3XcKKRcH3YdrbbgEQiBkcukHMfrIjClgM7JnkaTZbVAEinKMI0HxbkDziqzN/cP1ARvCieMbnUcf/6043DhqeOx9tW9GJXP4Pxpx2H2aRNw4anjPccSQhpDLARPLpfDueeeizVr1mD+/PkAgEqlgjVr1mDRokWe4/P5PPL5vOd2cvQ58bgR+Mysk/GZWSdjqFTGa7sPOcL9gtZcGieMbsXOA1UR8N4pYwH4mZbVRmGdhydrfeMPbjxYPd7r+ZENs7JAyqVTMIzqN+ShYhlwfft3nztQjQDs2DeAP+/tx3unjMWtq6rRnX88Z7JVth41zprcgQ+fNRGPvNSD2x/bgh989u/soaGKNVd1W7ZL0tUCplwxUa6YHkHq7pycDljvrHa0RPAsLUAd4RHRyanjveLOMAys+PQ5eH1vP07tbLM8SYSQY0ds3nVLlizBD3/4Q9x7773405/+hGuuuQb9/f244oorhvvUSI18Jo13n9Dh2TwEKh+PLi2km1Cu8/CICIA7QlDWeHhUKS2R7jAMp0AyDEPZ+TlI8IhrfWrrW1i/bR9y6RT+55x3eY6NEksuPhUpA3jsld3YuOOAPTRUMiwLVKJB55mRIzKyKNGltHQeHl1Vni6CNKRoPAioy+pV5myZEbkM3n1CB8UOIcNELCI8AHDZZZdh7969WLp0KXp6enD22Wdj1apVHiMzaV5OGT8KT76619okAb1oaNVUaek8PLpp6boNMOOT0sqmUx5vREs2Va2OkjxFommi23ANOHvxPPvGPgDAp953YuTTG9MmtOEfzpmM/7vhTXzr0S1Wh2FVVE+VFhrSRFTk9SyWK9b99vDQcMNi9dPS1cNJxeurNUSER5Tfq66VEDL8xEbwAMCiRYuUKSwSDU6Z4DUuB5elq8uUdX14wm6AGcU3ft0kdvt8ig4BpvMfAXaE56mtb6FcMTEil8b/mD3Nc1wU+ecPvgv/tXEnntr6liU8TlGk6dQRHrVnxil4TM+/dWXm3giPOD5cSmtA0XgQUKfj3BPhCSHNBWOrpGlQ9afRCx51lZY16yrj/sbv35dFF+GRN8yixuBcPZ96U1ojHY//38+f4ujPEmW6xo7AJ997IoDq9RkGrE7aMvWktNIpQ9kbSZeS1FVp2RGhYNOyaZq+ZenyuZumqWywSAhpHih4SNMgUgE79h+2NhqdaMhn/BsPuj08WY2nQ1Tx6D089gZYKKmjR9Xz8TYf9BM8Y0fmMLrmA2lvyeCqC6d6jokyC/9+miVKJ49pVfq2fCM8Ge/xQmjKaSdd52RVShKQ+y4Fe3iKZdPqkeM+H/vcqym7fbVqM524I4QMPxQ8pGk4bmQOHa1ZmKY9hDGoLH2wWHH0FNH24dGVNWtNr96yZl0FGFCtMqueTzjBYxgGzpjYDgD4wgdOUR4TZSa0teCK86s9qE6vXacb3whPTiV4vGkn7frphsUKgaRJacl9eOToYT6gLF1Ed04Y3Wq9FgghzUWsPDwk2hiGgVPGj8Rz2w/gz3sP4dTONhwcEsZfdUoLAIZKtolVP1pC/Y2/rEtxKCI89iR2hYenFgEYUAgedzpOcMulZ+IPr7+Ny2vpn7ixeM67MKEtj4tOm6C8X+WDsTwziudYFYXRdU7WprTK6giParSEEF+G4WyCCHjFmkjD0rBMSPNCwUOailPGj6oKnj39juodXYQHqG5MtuAJGB6qmZ7t9vCoqnwKvh4eUSYfzsMDAO/qbMO7OtuU98WBfCZtRXlU1OPhAdQRHl3nZO1oiYrOtOz18Ii1zGe8VXni3A8NlVAqVzxDQwkhzQdTWqSpkHvxiI1wRC6tKDNPWZucbBS2ozCaYZKaTr26FJjTtKz38NiNEMOltIiuLF1dpQXYxmI57VS21kQ9GsQ7ikItWu3hpPZ6+4mv9hb7u2LfYImCh5AIQMFDmgp5sGaQYGhRGIWFoVU/S8ud0tJ1WvZumEXNYwPe6e2DxbJ1LhQ8auTmfcKHFSbC4/BV6RpHpvzL0sPM0vIzUGfSKYyqDTztHShKFVo0LBPSrFDwkKZCjCB4/a1D2H+4AEAvGCyjsBRVCfTwhCxTTqtGS4RIaYlNUoi1dMqwNkbiRKxrsWxa3h0/wZNTmZY1jSN1Hh5dGbsqXSZeVzoTsjj/3X2D2HlgAAA9PIQ0MxQ8pKnoGtOKXDqFwWIFm3sOAtCbfvOKcQ66tJMqOlCp2GXH3m/8Xg+IrgLMeS7Ocvr2lox2YnXSGZlLW8+7eL50s7QAdRRG2zhSV5auEa0qD48YTOs2LAvaammtjTsOwDSB0SOy1tBbQkjzQcFDmopMOoWTx40AADz3l/0AfFJaWW9KS9cNWdW0Tv727zaxqjwgoTw8rggP01l6DMPwGJfFWuaVKa3ampS8a6JbP3eER5fSsqJHpXAeHsBeW/E6PWX8KIpbQpoYCh7SdAgfz3PbDwDwEzze3jdW2ikTHLGR/+1tXFdnHx6XaVk39JQ4sQRP7fkarIkZ9+wqQE47SWXpmpSkzsNjR4RcEcCMKqWlN1DL5y5ep/TvENLcUPCQpkMInrcODQEII3jkbshqUWJNS694N8vq/ZqUiMLD464Aq56LM9oU1IOHVHH34vH18ChESUnjyZE9PHJjSl0Zu9q0HC7CI16nrNAipLmh4CFNhxgiKghKaQ05TMvVzc2d0rJSHA7Dq70R6srS5eN1Yqp6LmoPDyM8/uhSWsqydIUosTsnqyN6gDPKU9KUsav78IgmiP6CR0DDMiHNDQUPaTqmjXc249OXpfuktNwpC0WKQ47euL7wayI8fh4edZUWIzz+6AWPj4dHIVq9VXb2zyVFGtMdEVJ1cdZNbnefu4ARHkKaGwoe0nRMHR82wlMb51CrpqlUTO1sJf9J24bHbKoaHurn4WGE58joaK1WOvW5q7R8IjyyaVnXOVkWNKqJ954Ups9oCW1Ka4S9trl0CpPHtCqPI4Q0BxQ8pOkYmc/g+I4W6+dAD09tkypK4sRblq735Lg3P/n3VaZl9yR2wFuWrht6SpxoIzyKNJJylpamc7IjwlP2RvV0rw/V8NAgDw8AnDxuhEd0EUKaC75DSVMipwd0aSG3UVje2LweHq+A0VXsAEGztMKntCh4/PEInpJfWbrXw6MrM884UlrBnh/xepEFsR1tUgse+XXJdBYhzQ8FD2lKZANo2CotOV2lbURX8aZDVBEee/ikPFqiJpBU09LdZekUPKHwRniCZ2mp0pJZlycnlTIsX5bKt6Wbll6umNbxAz4GavncARqWCYkCFDykKZF7moRtPCi++RuGyqMhqrSCe7gAkl9EOVpCL3iGGOGpC2uA6GAJwBFMS9dEbADbx1NUVGl5pqVLIlY8ZtiydIARHkKiAAUPaUrkDSSoSkuUpctVVB4TsmI2lr35eTfLtGI0gZ+Hp5Wm5SPC3YdHCEZV40Glh0eT0gLsdS2rPD+aUSLVx684zkU15gKg4CEkanCqIWlKTj++HblMCuNG5qyGc248Ka2SeqwEoJ6tpCtRBuqfpaVrPEjB44+c0ipXTOs59ovwFEqKlJaPD0uIHN/ZaSk5whM8uR0ARrdmMXpEFqWy6ekdRQhpPih4SFMydmQOD/2P830njbtFht80c9VsJX8PjzeaEGaW1kCxjMFiGUO1TZl9ePyRBY/cT8m3LF2OuvmkJW0fVnXd/GanpVIGMikDpYppp7QCqrQy6RT+85rzUKmYGJHjRykhzQ7fpaRpmT6p3ff+vCuN5BeBySqqcHQVO/Jtjj48otOyyrRcS69VTODt/gKAqpeozUewEVvwFEoVKyoGqMvSVQNd/dKSGVcKrORoW6D2bZUqZSuCFNR4EGAqi5AoQQ8PiSxyVAXwj8CkpW/7YrZSWVOxU73NW8YuNkxlHx5pU9zdNwgAaG/JIqV4bGIzKp+x1kY8b7l0Svm8qfvw6NOS7giP/Hvq3ktOQeU3uZ0QEj0oeEhkadWUpas8P7JHo+RKcaQVm6U8fFJQ8BFU+UwKwie9p89/6CmxMQwD7S3VKNju2vOW10RUVM0BrSidQsC4PTyyH8tdxg7Iw0mdHh6VgZoQEj0oeEhk8Xh4SsEeHsCO2viXpSuqtHyGhxqGgXxtw9xzsBqpoOAJh3iexPOm88yIVGKY0RKAdx6aWMuUAWUEye0RCmo8SAiJFhQ8JLJYvW9qG6Cfh0dOYQijaxj/h2oUherx5fMRqRkKnnCI50k8bzrPjMq0bIlWvzWsrXPRJ/0lP37B04eHH5OExAG+k0lkcU9L9/PwyLeJviz+Hh5vo0I7Zab25Yjz2c2UVl20W4Kn+rypDMuAfx+eMFVaZR+BC0genpJL8GjOhxASLSh4SGTRlaWr+vCkU4blsbEiPCFGS8gDSf08PADQmnNGeFiSHg53hEc8j278ZmmpojZuD49fCbv8+JaHp8SUFiFxgoKHRBbdLK2sJgLjjtrYk7YV/g9ptpIgKKUlPDxMadWHJ6Wliai4q6gAe9aZ2rflTGnpxkoIbNNyBcVyxVp7prQIiQd8J5PIIqp5BktlmKZp9U/RCRIRBbAa0fmNJfBJaQV7eJjSqgd3SktbpZVReHjCrGEl2KQOOCNIziaIjPAQEgcoeEhkERuRaVY3KT8PD+BtXOfr4VFEE/xGV1TPp3o7x0rUh3tiuk5gWB6ekiRCfaJ0aZeHpxTw+pAjSCJqCNiRO0JItOE7mUQWOfUxWKz4engA7zf+oo+HJ6tIaVkeHp1p2bVRU/CEw/08acvSrQn2inloymnpTg+P+Fu13o7HlyI81f5KbB5JSByg4CGRJZs2rM1rsFj2naUFeD0dZWu0hD464IjwBKW0MhQ8R4JH8GgiKm4Pj2maVlRPPS1d5+FRvz7kCNJQbY6WzkBNCIkeFDwkshiGYW2Og8Wybx8eAMh6vvHrU1qiE6+qD09QSktAwROOuiM8JWdbAUDdOVk3PFR1rPz4BSmlxZJ0QuIDBQ+JNHKlltgIVcM9ASBtRQjcoyXCTVcvWhEhprSOJl7BE1xFBbinn+tHS4gUmPg9bUpLevwBNh0kJHbw3UwiTYs0MT0oApN1VWmVfb7x21Va3vRJUJWWgIInHPVGeAoqwaNYQ5EC86x3UONBycPDCi1C4kNmuE+AkHdCXmo+GOzhcYoYq6TZp4dLxQQqFdOxuYYVPKNa+PYKg7tBo17wOD088pwzdYTHNVoiqA+P1HhQpLQ4KZ2Q+MAID4k01niJUiXQwyM2wKL1jV/fl8UxbLRiOszLYTw8bS0ZbeqEOGnLZyAXQgWWpbtSkkC40RJhq7QKJSnCw5J0QmID380k0rQoIzz+VT5la9SAfiyBvIGWKhWH4NFFkOSNmums8KRSBtpb7OcraHhouWKiXDEdTQdVpePu8SDBKS1vWTpTWoTEBwoeEmkcHp6S/4ZmbYDu4aHKHi72W6NUMa3okWHoIwRyNICCpz7k50s7WkJ6fovlSmDnZLGuZXdKS1ulJXl4rDla/IgkJC7w3UwijRA8Q1LjwaDREu6+LH5jCcRxsmFZ14iOEZ4jxyF4Ajw8QE3wBJjI0+7REmV/dwIRagAAIABJREFUgSQPDx1ihIeQ2EHBQyJNa21DGgjRh8cuNXd23lVtgKmUAXFzqVwJHCsBUPC8E5yCx7/KDqiKkiBPjiVw3X2XAlJa8iytVgoeQmIDBQ+JNMoqLY3R1NN518fD4zheMi3r0mWAc6Om4KmPMBGeVMqQ0pIVu5FgQArTE+HRebxqI0OKJanxIAUPIbGBgodEGrnxoBAyucANsGZiDRg1YHVmLpuB0SPAWcJMwVMf7SEiPICzkqoU4MlJuzw8fp21ATt6V6qYVuNB3eR2Qkj04LuZRBq7LD1ESsv9jd+n07J8e7ESPIldPhfA21uG+CMLxLzPOAfZWBzUOVm33nrTsjelxdEShMQHCh4SaeorS3entMKZWMtSSivn05dFHjTJCE99yM+X38BOe7yEGVhm7vHwBKQl7VldTGkREkcoeEikcczSClm1457FFFTWXJRMy/TwNIYwHh7AFjHVCI9/52R340G/yeqAuyyds7QIiRt8N5NIIzakIXmWViagL4votGyNlgguYw/j4ZHTHxQ89eHsw+Pj4amtbSFEH5502vZgAXLjwaDhpCxLJySOcNgPiTRWhKdURqFUr4cnXOO6apVWCA8PTctHTNgIj5x2Ciozd693MexoCamrNiM8hMQHCh4SaSzTcpjGg9LoACBESkuamB40iR1gSuudEFbwyPO0gqq0bA+Ps9FkUB+eYrmCSu13aFomJD5Q8JBI05KTRksERGGyLk+H32gJwLlh2j1+9B6e1lwaKaM6YX3MiFy9l5Joxo6qPl8t2ZTv0FVZlAR1Ts64ZqdZKa0QoyWKtdtafAzUhJBoQcFDIo3wewzIHp6gaenWbKWK43Y3ckorKF0GVMupv/LhM1Asm+gYwQhPPZwwuhX/84PvQmd73vc4IUoK5eCUlm1Sd6+3fx+eYsnu4swIDyHxgYKHRBpnlZZ/FMY9Ld3+xq+LEAjTstzV19/TceUFU+s5fSKx5OJTA49xRHgqAW0IUnZbAflvbVl6xn7sIQ4PJSR28N1MIo09PDSEaTnt/MYf1HhQnq4exsNDGk9OEiVBZebu4aFBZeyyaXmoxCotQuIGIzwk0jgbD4rREv4prZIrwhNU5VN2pLT0/hLSeLJS2qlsBs1Cc0b0ghtNSn142HiQkNhBwUMijV2WHlyl5TYtF4OqfKTp6mHK0knjkT08phlUZef0bIWdpVUsm/ZoCaa0CIkNFDwk0ghT6UChHDw9O+3cAMtBfXikDTNoEjs5NsgenpreCTQtl62y9IBp6bXb5dcSTcuExAcKHhJpxDdwMd0a0IsSua8OEOzhkU3O9PA0B9ZE85poBepoNFn2j/BkM97XElNahMQHCh4SaVR9UnSiRC4zB4Ib0cllzfZoCXp4hhPZWGzUlkJrWk6rBa4+wuN9nDwjeoTEBgoeEmlUKYegTsvu2Up6D49dll4s0cPTDIiWA8VyBama4tGWmbvK0u0ydn8PjyCfSSHl0wSREBIt+OlNIk02bUDek1JGcJl5yVW1o01pSSmRIEM0OTY4+/D4C1ZdWXrQLC0B01mExAt+epNIYxiGY2PyEyRuT0dQWXpaMVoixxTHsOKcpeUvWO2y9HARPa/g4VoTEica9o7+5je/ifPOOw8jRozA6NGjlcds374d8+bNw4gRIzBhwgR86UtfQqlUchzzxBNP4JxzzkE+n8e0adOwcuVKz+MsX74cJ598MlpaWjBz5kw888wzjbgk0qTIgsfPVJx1pbSCytKzkgekEDC3iRwbLA9PqRJclZey01+A7eXRpsBctzPCQ0i8aJjgKRQK+PjHP45rrrlGeX+5XMa8efNQKBTw9NNP495778XKlSuxdOlS65ht27Zh3rx5uOiii7Bx40YsXrwYV155JR599FHrmPvvvx9LlizBTTfdhOeeew4zZsxAd3c39uzZ06hLI01GixR18SsbT7s2wHJAXxbZ5Mw+PM2Bc3iovwk54/LwBKW0DMNwiB6WpBMSLxr26f21r30N1157Lc466yzl/Y899hheeeUV/OQnP8HZZ5+ND33oQ/j617+O5cuXo1AoAABWrFiBKVOm4Pbbb8cZZ5yBRYsW4R//8R9xxx13WI/z7W9/G1dddRWuuOIKTJ8+HStWrMCIESNw9913N+rSSJPhTGn5Tdp29WUJ8PBY09LLJool9uFpBmTTclDnZLeHx56lFRwFBJjSIiRuDNs7et26dTjrrLPQ2dlp3dbd3Y2+vj5s2rTJOmbOnDmO3+vu7sa6desAVKNIGzZscByTSqUwZ84c6xgSf/KS4NGlp+T7iiHL0q2UiKMPD1Naw4ns4QndKbu2dsUAgeS+L8+UFiGxYtjK0nt6ehxiB4D1c09Pj+8xfX19GBgYwP79+1Eul5XHbN68Wft/Dw0NYWhoyPq5r6/vHV0LGV7kb+J+pmK5L4tpmoFVPiJVUnb04eG3/uFE7sMjInZBgjVs3yXA+fqhh4eQeFHXp/eXv/xlGIbh+8dPaDQLy5YtQ0dHh/Wnq6truE+JvANaw6a0JE9HxW7U6zNagmXpzYY9PLQS2DnZ7eEJqtKSHx8AWpnSIiRW1BXhue666/D5z3/e95ipU6eGeqyJEyd6qql2795t3Sf+FrfJx7S3t6O1tRXpdBrpdFp5jHgMFTfccAOWLFli/dzX10fRE2FCl6VL07CFgAHsyI//8TQtNwPyRPNiQOdkO6JnWr9TPd7P58UIDyFxpS7BM378eIwfP/6o/MezZs3CN7/5TezZswcTJkwAAKxevRrt7e2YPn26dcwjjzzi+L3Vq1dj1qxZAIBcLodzzz0Xa9aswfz58wEAlUoFa9aswaJFi7T/dz6fRz6fPyrXQYYfOaUVtg9PWQrxZAP6spQdfXjo4RlORMqpWDat4a/6TsvuRpNhIjys0iIkrjTs6+r27duxceNGbN++HeVyGRs3bsTGjRtx6NAhAMDcuXMxffp0fOYzn8ELL7yARx99FDfeeCMWLlxoiZEvfvGLeP3113H99ddj8+bN+N73vocHHngA1157rfX/LFmyBD/84Q9x77334k9/+hOuueYa9Pf344orrmjUpZEmQ96Y/PrwyKMlSpLg0c5ikmdplZjSagZkD09Qmbm4vWIClYopTUsPG+HhWhMSJxpmWl66dCnuvfde6+e//du/BQA8/vjjmD17NtLpNB5++GFcc801mDVrFkaOHInPfe5zuOWWW6zfmTJlCn7961/j2muvxZ133onJkyfjRz/6Ebq7u61jLrvsMuzduxdLly5FT08Pzj77bKxatcpjZCbxRa6myfpEYOTREnKEJ9jDU6GHp0mQmwlajQR1pnPp9rJkUtcdD9C0TEicaZjgWblypbIrssxJJ53kSVm5mT17Np5//nnfYxYtWuSbwiLxJnRKS/J0iM0yZUA7INLqzMzGg01D1kppSbO0AjxYgFjzWkQoZISHZemExAt+epPIE36Wli1gwvg5rMZ1ZbkPD98yw4nVh6ckCZiAlBZQjdJZ09J9+vA4PDxMaRESK/iOJpEnrIdHno0lUlq6zdJ5vFSWTtPysOKclu6fZpRTlcWy3YpAV9XlfiyalgmJFxQ8JPI4U1p6QWKZkKWqK/+uu3ZEiKbl5kCsb0FOaYWI8AwWy8rb3eRYlk5IbOGnN4k8rblwKS25zLwc4P+Q76ualqvHM6U1vKiHh+qHgQoxJAse/3lrUuPBHNeakDjBdzSJPHLqwW+4p9j8ypIJOR1i9pYjpUXBM6zIfXjq8WENFu1Gk759eDJMaRESV/jpTSJPXp6lFcK0DACDpXLttuAIj1wR5BcdII3HOVoiuK+OFeEplT23qR9fNi1T8BASJyh4SORpCTlLS94YRYojzGZ5uCClQ3wiSKTxqD08wc0mxXr7tSEAnII5zyotQmIF39Ek8tQ7SwsAhoohTMuuzRKgh2e4ySmqtMKIVmu9A9aPs7QIiS/89CaRp0WKuoTpwwPYIsa3LL1234DD8Mq3zHAinv+KaYsYv87JaZdp2U/gyo8P0MNDSNzgpzeJPPI38ZxPyimdMmDU9jvbwxO8WYqUVsrwF0ik8cgpxYEQotXt4QkUPBnZw8OPR0LiBN/RJPKE9fAAdjRgsBgiHeJKaTG6M/xkFT4sf9+Wc72D1pB9eAiJL/wEJ5En7CwtwI4GDIVIcWStKi324GkW5PRV0erDE9yKYChENAigh4eQOMNPcBJ5WkOalgE7ojNY65zstwG672OF1vCTShkekeonWi0PT8hO2Y7GgxQ8hMQKfoKTyCNPtQ6KwojNcaAgytLDzVWq/kz/TjPgXpcwaUmx3sERHvv+PAUuIbGC72gSeRwprYDhnmIDHCoFl6V7IjxMaTUFbuEZxrRsrXeAaBWm91wm5duvhxASPfgJTiJPLp2yqq8CUxauMmX/snTnY9HD0xy4K/HqKUv3OxawXz8tjO4QEjv4riaRxzAMq2dKoGk5Lb7xB1deuaMBjPA0B/WktLKu9Q5rWqZhmZD4wU9wEgtEWisoCuMuSw+TDrF+poenKfAInjqGhwa2LajdT8FDSPyg4CGxQGxQQaLEqtIKUZbuNjQzwtMcuEWL/2gJZy+lsKMl2HSQkPjBdzWJBW0tGQDAiJz/N/O0awP0jfC4NlJ6eJoDb4QnRFl6yD484vUzKp95J6dICGlC+K4mseD67tOxftvbOLtrjO9x2bQ7xRHctM763YAKMHJskE3L1XEhwR6esCmt9009DlecfzI+eHrnUThTQkgzQcFDYsGc6Z2YMz14k3LPVvL38DCl1YzI6xA0GyvtWm8/vw9QTY3e9NEz3+EZEkKaEX6Ck0SRcc/SqsO0TMHTHMjrEthZu471JoTEG36Ck0QhfDnWLC2fFEcqZUDeH+nhaQ7cKS0/6llvQki84Sc4SRTuCehBKQ65qoejJZqDbB1r4jYtB1VpEULiC9/9JFHYHp7gPjyA3ZkZYEqrWZBFTqBgda03U1qEJBd+gpNEkXF/4w9pegU4Lb1ZkIVnkGB1tyEIEkiEkPjCdz9JFFl3Siuw8679FqGHpznI1ZHSyroaTTItSUhy4Sc4SRQiIlAxxc9BHh45pcXNshlwlKUHzU7zrDfXkJCkQsFDEoU7ohOU0pJTIPTwNAdyA8jg9WNrAUJIFb77SaLIuiI6YWdvAdwsmwVnhCdo/cKPoSCExBt+gpNEka47wmPfn6NpuSnIOToth6vSErjXnxCSHPgJThJF1r0BBm6Y7MPTbBzJaAnrd1mlRUhi4bufJIp6UxxMaTUfdaW0XOvLTsuEJBd+gpNEUe8G6Oy0zLdLMyCblgNnadHDQwipwU9wkijqr9KSPDwUPE1Bro7Gg16ByzUkJKnw3U8ShdvkGuzhkTstMzrQDGTrMC27BREjPIQkFwoekii8fVnCd1pmSqs5qGd4KFNahBABP8FJonBvgMGzmGhabjZkkcOUFiEkLHz3k0ThjggEfeOXj6eHpzmQ+yEFiVBPWTqrtAhJLPwEJ4nC6+mopw8P3y7NQD19eNwCJ8izRQiJL3z3k0ThSWkFfONPc3ho01FPHx63wOEaEpJcKHhIonB3Wg6MEDiqtPh2aQZk0VLvaImg4wkh8YXvfpIo3CmtQNOrFE2gh6c5yNUV4alvvQkh8YWf4CRRuH04gZ16WaXVdMiRtno9PExpEZJc+AlOEoU7IhAc4TGU/ybDh9PDE1Sl5erDQ9FKSGLhu58kCq+nI6iPC1NazYbTw1NnHx6mtAhJLPwEJ4nCbVqtx/TKlFZzUM9oCQoeQoiAn+AkUXiGh9Y1LZ2bZTNQT1m6d735kUdIUuG7nyQK7/DQ8CkRlqU3B/WktDweHkZ4CEks/AQnicLzjb8O0zI9PM1Brg7TsneWFgUPIUmFn+AkUXhmaQVsmJyW3nzUNy3dXZbONSQkqfDdTxJFvSkOkfJKGWxa1yzIqcV6p6VzDQlJLhQ8JFHUuwGK4xkZaB7kqE42oErLM0uLoyUISSx895NE4UlxBGyAQujQv9M8yGsWWKXlFrj08BCSWPgpThKFp0or5CwmVmg1D6mUYQmZejplA97hsYSQ5MBPcZIoPKblkLOY2IOnuRCRt6BUo1sQsQ8PIcmF736SKDwbYMjREvTwNBdCgAYK1jr7LhFC4gs/xUmicAuXsCkReniai1wtxRjk4XGnLBmpIyS58FOcJAo5IpBOGTAMRniiiFiP+mdpcR0JSSp895NEIW94YdIbIoKQzTAy0ExYgiek6VzA0RKEJBcKHpIoMo4eLsGb34ljRzj+Js3BSceNgGEAXWP810X28KSMaoUXISSZZIb7BAg5lsiCJ0yE54zj2/Hb6z6ASaNbG3lapE5WfPpc7D04hK4AIZpKGTAMwDRZoUVI0mnYJ8Abb7yBBQsWYMqUKWhtbcUpp5yCm266CYVCwXHciy++iAsuuAAtLS3o6urCrbfe6nmsn//85zj99NPR0tKCs846C4888ojjftM0sXTpUhx//PFobW3FnDlz8NprrzXq0kiEyTia1oV7+U8dPwot2XSjTokcASPzGZw8bmSoY0Uai+ksQpJNwwTP5s2bUalU8G//9m/YtGkT7rjjDqxYsQJf+cpXrGP6+vowd+5cnHTSSdiwYQNuu+023HzzzfjBD35gHfP000/jE5/4BBYsWIDnn38e8+fPx/z58/Hyyy9bx9x666246667sGLFCqxfvx4jR45Ed3c3BgcHG3V5JKKka9/4AW6ASUGIXK43IcnGME3TPFb/2W233Ybvf//7eP311wEA3//+9/HVr34VPT09yOVyAIAvf/nLeOihh7B582YAwGWXXYb+/n48/PDD1uO8733vw9lnn40VK1bANE1MmjQJ1113Hf7lX/4FANDb24vOzk6sXLkSl19+eeB59fX1oaOjA729vWhvbz/al02ajFO/+v+hUK5gUkcLnr7hg8N9OqTBnHXTozg4VMJxI3PY8L8uHu7TIYQcRerZv49pUru3txdjx461fl63bh0uvPBCS+wAQHd3N7Zs2YL9+/dbx8yZM8fxON3d3Vi3bh0AYNu2bejp6XEc09HRgZkzZ1rHuBkaGkJfX5/jD0kOwrvDuUrJQKwzmw4SkmyOmeDZunUrvvvd7+ILX/iCdVtPTw86Ozsdx4mfe3p6fI+R75d/T3WMm2XLlqGjo8P609XV9Q6ujESNjNWllybWJMCJ94QQ4AgEz5e//GUYhuH7R6SjBDt37sQll1yCj3/847jqqquO2skfKTfccAN6e3utPzt27BjuUyLHELtpHb/xJwHLw8OIHiGJpu6y9Ouuuw6f//znfY+ZOnWq9e9du3bhoosuwnnnnecwIwPAxIkTsXv3bsdt4ueJEyf6HiPfL247/vjjHcecffbZyvPL5/PI5/O+10DiSzrkpG0SD7jehBDgCATP+PHjMX78+FDH7ty5ExdddBHOPfdc3HPPPUi5UgizZs3CV7/6VRSLRWSzWQDA6tWrcdppp2HMmDHWMWvWrMHixYut31u9ejVmzZoFAJgyZQomTpyINWvWWAKnr68P69evxzXXXFPv5ZEEIBoO8ht/MrC6ZTOFSUiiadgnwM6dOzF79myceOKJ+Na3voW9e/eip6fH4av55Cc/iVwuhwULFmDTpk24//77ceedd2LJkiXWMf/8z/+MVatW4fbbb8fmzZtx8803449//CMWLVoEADAMA4sXL8Y3vvEN/PKXv8RLL72Ez372s5g0aRLmz5/fqMsjESYTcg4TiQcZClxCCBrYaXn16tXYunUrtm7dismTJzvuE5XwHR0deOyxx7Bw4UKce+65GDduHJYuXYqrr77aOva8887DfffdhxtvvBFf+cpX8K53vQsPPfQQ3v3ud1vHXH/99ejv78fVV1+NAwcO4P3vfz9WrVqFlpaWRl0eiTBsRJcs2IeHEAIc4z48zQr78CSLuXc8iVd3H8LMKWNx/xdmDffpkAbz4Tt/h1f+2odzTxqD/7zmvOE+HULIUaRp+/AQ0gyIb/wsU04G2TQjeoQQCh6SQDJsRJco0vTwEEJAwUMSCD08ycL28PDjjpAkw08AkjhElRYjPMkgbXVa5noTkmQoeEji4KiBZMEUJiEEoOAhCYQRnmRh9+Hhxx0hSYafACRxZOnhSRRpUZXH9SYk0VDwkMTBqp1kkbVSWvy4IyTJ8BOAJI6sldLiyz8J0LRMCAEoeEgCybARXaLgLC1CCEDBQxKI+MZP03IySLMPDyEEFDwkgWSt0RIUPEmAoyUIIQAFD0kgGZpYE0WaZemEEFDwkAQyekQWANDRmh3mMyHHAq43IQQAMsN9AoQca/77+VPQ2d6CS2ecMNynQo4BXG9CCAAYpmmaw30Sw01fXx86OjrQ29uL9vb24T4dQgghhISgnv2bKS1CCCGExB4KHkIIIYTEHgoeQgghhMQeCh5CCCGExB4KHkIIIYTEHgoeQgghhMQeCh5CCCGExB4KHkIIIYTEHgoeQgghhMQeCh5CCCGExB4KHkIIIYTEHgoeQgghhMQeCh5CCCGExJ7McJ9AMyAGxvf19Q3zmRBCCCEkLGLfFvu4HxQ8AA4ePAgA6OrqGuYzIYQQQki9HDx4EB0dHb7HGGYYWRRzKpUKdu3ahba2NhiGcVQfu6+vD11dXdixYwfa29uP6mM3A3G/PiD+18jriz5xv8a4Xx8Q/2ts1PWZpomDBw9i0qRJSKX8XTqM8ABIpVKYPHlyQ/+P9vb2WL6IBXG/PiD+18jriz5xv8a4Xx8Q/2tsxPUFRXYENC0TQgghJPZQ8BBCCCEk9qRvvvnmm4f7JOJOOp3G7NmzkcnEM4MY9+sD4n+NvL7oE/drjPv1AfG/xuG+PpqWCSGEEBJ7mNIihBBCSOyh4CGEEEJI7KHgIYQQQkjsoeAhhBBCSOyh4DkCli9fjpNPPhktLS2YOXMmnnnmGd/jf/7zn+P0009HS0sLzjrrLDzyyCOO+03TxNKlS3H88cejtbUVc+bMwWuvvdbIS/Clnuv74Q9/iAsuuABjxozBmDFjMGfOHM/xn//852EYhuPPJZdc0ujL0FLP9a1cudJz7i0tLY5jmm39gPqucfbs2Z5rNAwD8+bNs45ppjVcu3YtPvrRj2LSpEkwDAMPPfRQ4O888cQTOOecc5DP5zFt2jSsXLnSc0y97+tGUe/1Pfjgg7j44osxfvx4tLe3Y9asWXj00Ucdx9x8882e9Tv99NMbeRla6r2+J554Qvn67OnpcRzXLOsH1H+NqveXYRg488wzrWOaaQ2XLVuG97znPWhra8OECRMwf/58bNmyJfD3hnsvpOCpk/vvvx9LlizBTTfdhOeeew4zZsxAd3c39uzZozz+6aefxic+8QksWLAAzz//PObPn4/58+fj5Zdfto659dZbcdddd2HFihVYv349Ro4cie7ubgwODh6ry7Ko9/qeeOIJfOITn8Djjz+OdevWoaurC3PnzsXOnTsdx11yySX461//av352c9+diwux0O91wdUO4PK5/6Xv/zFcX8zrR9Q/zU++OCDjut7+eWXkU6n8fGPf9xxXLOsYX9/P2bMmIHly5eHOn7btm2YN28eLrroImzcuBGLFy/GlVde6RAFR/K6aBT1Xt/atWtx8cUX45FHHsGGDRtw0UUX4aMf/Sief/55x3FnnnmmY/2eeuqpRpx+IPVen2DLli2O858wYYJ1XzOtH1D/Nd55552Oa9uxYwfGjh3reQ82yxo++eSTWLhwIf7whz9g9erVKBaLmDt3Lvr7+7W/0xR7oUnq4r3vfa+5cOFC6+dyuWxOmjTJXLZsmfL4f/qnfzLnzZvnuG3mzJnmF77wBdM0TbNSqZgTJ040b7vtNuv+AwcOmPl83vzZz37WgCvwp97rc1Mqlcy2tjbz3nvvtW773Oc+Z1566aVH/VyPhHqv75577jE7Ojq0j9ds62ea73wN77jjDrOtrc08dOiQdVszraEMAPMXv/iF7zHXX3+9eeaZZzpuu+yyy8zu7m7r53f6nDWKMNenYvr06ebXvvY16+ebbrrJnDFjxtE8taNCmOt7/PHHTQDm/v37tcc06/qZ5pGt4S9+8QvTMAzzjTfesG5r1jU0TdPcs2ePCcB88skntcc0w17ICE8dFAoFbNiwAXPmzLFuS6VSmDNnDtatW6f8nXXr1jmOB4Du7m7r+G3btqGnp8dxTEdHB2bOnKl9zEZxJNfn5vDhwygWixg7dqzj9ieeeAITJkzAaaedhmuuuQZvv/32UT33MBzp9R06dAgnnXQSurq6cOmll2LTpk3Wfc20fsDRWcMf//jHuPzyyzFy5EjH7c2whkdC0HvwaDxnzUSlUsHBgwc978HXXnsNkyZNwtSpU/GpT30K/387dxfS1B/GAfz7T3fULmrEYltvY0qOKIe9sLFVTNAiu6mr9EKRyIJISKjImxDxZsLIi5BeILNXx0pqULRMbV6MXiAXzbJoJoWURoE507pwz/+i/w6d5tumttP+zwfGtt+e/fZ79vzOzm/b2d6/f5+gEcYnNzcXWq0W27Ztg8/nE9uTrX7Az22woKAAOp1O0i7XGn79+hUAoubcr+SwL+QFTww+f/6M8fFxqNVqSbtarY76PjliYGBgyvjIeSx9zpd48vvd8ePHsWzZMsmk3bFjBy5duoT29nbU1dWhs7MThYWFGB8fn9PxTyee/AwGAxobG+F2u3HlyhWEw2FYrVb09/cDkFf9gNnX8MmTJ+ju7kZ5ebmkXS41jMdk2+Dw8DDGxsbmZN7LicPhwMjICPbs2SO2mc1mNDU1wePx4PTp0+jr68PWrVsRCoUSONKZ0Wq1OHPmDFpaWtDS0oKVK1ciLy8PXV1dAObmdUtOPnz4gLt370Ztg3KtYTgcRmVlJTZv3ox169ZNGieHfWFy/n81Swi73Q6n0wmv1ys5sLe4uFi8nJOTA6PRiKysLHi9XuTn5ydiqDObdKSiAAAE90lEQVRmsVhgsVjE61arFWvWrMHZs2dRW1ubwJHNj/PnzyMnJwcmk0nS/jfX8P/k2rVrqKmpgdvtlhzjUlhYKF42Go0wm83Q6XRwuVzYt29fIoY6YwaDAQaDQbxutVrR29uL+vp6XL58OYEjmx8XL16EUqnE7t27Je1yreGhQ4fQ3d2dsOOJYsGf8MRApVIhJSUFg4ODkvbBwUFoNJoJ76PRaKaMj5zH0ud8iSe/CIfDAbvdjtbWVhiNxiljMzMzoVKpEAwGZz3mWMwmvwiFQoH169eLY5dT/YDZ5fjt2zc4nc4ZvXgmqobxmGwbXLRoETIyMuZkXsiB0+lEeXk5XC5X1FcHv1MqlcjOzv4r6jcRk8kkjj1Z6gf8/JVSY2MjSktLIQjClLFyqGFFRQVu376NBw8eYMWKFVPGymFfyAueGAiCgI0bN6K9vV1sC4fDaG9vl3wK8CuLxSKJB4D79++L8Xq9HhqNRhIzPDyMx48fT9rnfIknP+DnkfW1tbXweDzYtGnTtI/T39+PL1++QKvVzsm4Zyre/H41Pj6OQCAgjl1O9QNml+P169fx48cPlJSUTPs4iaphPKbbBudiXiRac3Mz9u7di+bmZsnfCUxmZGQEvb29f0X9JvLs2TNx7MlQv4jOzk4Eg8EZvelIZA2JCBUVFbh58yY6Ojqg1+unvY8s9oVzcujz/4jT6aS0tDRqamqily9f0oEDB0ipVNLAwAAREZWWllJVVZUY7/P5KDU1lRwOB/X09FB1dTUpFAoKBAJijN1uJ6VSSW63m54/f067du0ivV5PY2Njss/PbreTIAh048YN+vjxo3gKhUJERBQKhejo0aP08OFD6uvro7a2NtqwYQOtXr2avn//Lvv8ampq6N69e9Tb20tPnz6l4uJiSk9PpxcvXogxcqofUew5RmzZsoWKioqi2uVWw1AoRH6/n/x+PwGgkydPkt/vp3fv3hERUVVVFZWWlorxb9++pYULF9KxY8eop6eHGhoaKCUlhTwejxgz3XMm5/yuXr1Kqamp1NDQINkGh4aGxJgjR46Q1+ulvr4+8vl8VFBQQCqVij59+iT7/Orr6+nWrVv05s0bCgQCdPjwYVqwYAG1tbWJMXKqH1HsOUaUlJSQ2WyesE851fDgwYO0ePFi8nq9kjk3OjoqxshxX8gLnjicOnWKVq1aRYIgkMlkokePHom32Ww2Kisrk8S7XC7Kzs4mQRBo7dq1dOfOHcnt4XCYTpw4QWq1mtLS0ig/P59ev379J1KZUCz56XQ6AhB1qq6uJiKi0dFR2r59Oy1dupQUCgXpdDrav39/wl6IiGLLr7KyUoxVq9W0c+dO6urqkvQnt/oRxT5HX716RQCotbU1qi+51TDyM+XfT5GcysrKyGazRd0nNzeXBEGgzMxMunDhQlS/Uz1nf1Ks+dlstinjiX7+DF+r1ZIgCLR8+XIqKiqiYDD4ZxP7T6z51dXVUVZWFqWnp9OSJUsoLy+POjo6ovqVS/2I4pujQ0NDlJGRQefOnZuwTznVcKLcAEi2KznuC//5b/CMMcYYY0mLj+FhjDHGWNLjBQ9jjDHGkh4veBhjjDGW9HjBwxhjjLGkxwsexhhjjCU9XvAwxhhjLOnxgocxxhhjSY8XPIwxxhhLerzgYYwxxljS4wUPY4wxxpIeL3gYY4wxlvR4wcMYY4yxpPcv7gJq0QkJRw4AAAAASUVORK5CYII=",
            "text/plain": [
              "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1-element Vector{PyCall.PyObject}:\n",
              " PyObject <matplotlib.lines.Line2D object at 0x7fbf30a5b790>"
            ]
          },
          "metadata": {},
          "execution_count": 48
        }
      ],
      "source": [
        "# unstable when |CFL|>1\n",
        "diffusion_1D_theta(81; theta=1/4, sigma=2)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "diffusion_1D_theta(81; theta=1/4, sigma=0.6)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 466
        },
        "id": "mK1YRWNczf5W",
        "outputId": "c4d1d64a-e656-4622-d93d-30093ab27845"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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",
            "text/plain": [
              "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1-element Vector{PyCall.PyObject}:\n",
              " PyObject <matplotlib.lines.Line2D object at 0x7fbf30a08210>"
            ]
          },
          "metadata": {},
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 466
        },
        "id": "te16D9UHFmG5",
        "outputId": "d9928379-2293-4e47-b52e-186b1d4726b9"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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",
            "text/plain": [
              "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1-element Vector{PyCall.PyObject}:\n",
              " PyObject <matplotlib.lines.Line2D object at 0x7fbf2c5b7490>"
            ]
          },
          "metadata": {},
          "execution_count": 50
        }
      ],
      "source": [
        "diffusion_1D_theta(81; theta=1, sigma=0.6)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 466
        },
        "id": "Qo4heePs_BO1",
        "outputId": "d831e3c9-d926-48ed-cf01-653e1c093e7c"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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PjUFggFpyNd5j0qBohGjVqGrqwMEzjbLLISIfxDBCfuObroXObuTGeE4JDFBj+lBbV8033DiPiNyAYYT8QkVDO45XNUNRgGkZMbLL8TozhtnCyLcnqiVXQkS+iGGE/MLmrjfRrORwRIRoJVfjfewB7tCZRpxr7pBcDRH5GoYR8gvfnrB10czo6m4g58SE6TA6ybZ0/ha2jhCRizGMkM8zmi3YVmhbztze3UDOs48b2cwwQkQuxjBCPm93cT3aTBbEhOkwPEEvuxyvNWOorasmt6AanVyNlYhciGGEfJ69i2Z6Rgw3xrsKo5PCERmiRXOHGftK62WXQ0Q+hGGEfN5m+3gRdtFcFbVKcQxk5awaInIlhhHyaWW1bThV3Qq1SsEUrrp61aZ3ddXYAx4RkSswjJBP23zS9qY5LiUC+sAAydV4v+uGxEClAMermlHR0C67HCLyEQwj5NO+Pc4uGleKCNEia2AEAM6qISLXYRghn9XRacH2U7UAuL6IK9ln1XzLrhoichGGEfJZeUW1MJqtSDQEIiMuVHY5PsO+3si2whoYzRbJ1RCRL2AYIZ+1uauLZvqwWCgKp/S6yohEPWLDdGgzWbC7mFN8iejqMYyQTxJCOKafsovGtRRFccyqYVcNEbkCwwj5pKKaVpTVtUGrVmHy4CjZ5fgce8BjGCEiV2AYIZ9kn0WTnR6JYK1GcjW+Z/KQaGhUCoqqW1Fa2yq7HCLycgwj5JM2s4vGrfSBARiXyim+ROQaDCPkc1qNZuws7prSy/VF3IZdNUTkKgwj5HO2n6pFp0UgJSoYadEhssvxWfagl3eqFh2dnOJLRH3HMEI+57sCW7fBdUNiJFfi24bEhiJOr4PRbMXukjrZ5RCRF2MYIZ+ztaAGADCVG+O5laIomNoV+Oz/5kREfcEwQj7ldH0bimpsu/ROHMQpve5mD3y5DCNEdBUYRsin2D+hj0kO5y69/WDyYFsYOVbZhOpmo+RqiMhbMYyQT/mu0BZGpgxmF01/iA7V4ZoEPQBg+ym2jhBR3zCMkM+wWAW2dYWR6zIYRvrLdV1dNd+xq4aI+ohhhHzGkYpGNLR1IkynQWZSuOxy/MYURxiphhBCcjVE5I0YRshn2D+ZTxwUBY2aL+3+Mj41ElqNCmebjCg81yK7HCLyQvyLTT7DPnj1Ok7p7VeBAWpkp0UCYFcNEfUNwwj5hDaTGXtKbQtvTeFiZ/3OPmDYvuAcEZEznA4jubm5mDdvHhITE6EoCtatW3fFxxiNRvz3f/83UlJSoNPpkJqaijfffLNPBRNdys7iOnRaBAaEByE1Klh2OX7HPm5kZ3EdTGar5GqIyNs4vbd6a2srMjMz8cgjj+COO+7o1WPmz5+Ps2fP4o033sDgwYNRWVkJq5V/sMh1Llx1VVEUydX4n2vi9YgK0aK21YR9ZfWYmM4F54io95wOI3PmzMGcOXN6ffz69euxZcsWFBUVITLS1q+cmprq7NMSXZa9e2Aqu2ikUKkUTBkSjU/yK/BdQTXDCBE5xe1jRj799FOMGzcOL774IgYMGICMjAz88pe/RHt7e4+PMRqNaGpq6nYj6snZpg6cPNsCRQEmcQl4aezjRrhPDRE5y+mWEWcVFRVh69atCAwMxNq1a1FTU4Of/exnqK2txVtvvXXJxyxfvhzLli1zd2nkI+xvfqMGGBARopVcjf+yt0odPNOIhjYTwoN5LYiod9zeMmK1WqEoCt577z1MmDABN998M15++WW8/fbbPbaOLF68GI2NjY5beXm5u8skL7a1kLv0eoJ4QyCGxIZCCGD7qVrZ5RCRF3F7GElISMCAAQNgMBgc911zzTUQQuD06dOXfIxOp4Ner+92I7oUIYRjbYspgzleRLYLV2MlIuott4eRyZMno6KiAi0t51dmPHnyJFQqFZKSktz99OTjjlc1o6bFiKAANcamcAl42aZesE8Nl4Ynot5yOoy0tLQgPz8f+fn5AIDi4mLk5+ejrKwMgK2LZcGCBY7j7733XkRFReHhhx/G0aNHkZubi6effhqPPPIIgoKCXHQa5K/s40Wy0yOh06glV0PZaVEIUCs4Xd+O0to22eUQkZdwOozs2bMHWVlZyMrKAgAsWrQIWVlZWLJkCQCgsrLSEUwAIDQ0FBs3bkRDQwPGjRuH++67D/PmzcNrr73molMgf5bLKb0eJUSnwdiBEQDYVUNEvef0bJrp06dftvl15cqVF903bNgwbNy40dmnIroso9mC3SW2JeA5eNVzTB0SjZ3FddhaWIMHclJll0NEXoB705DX2l/WgI5OK2LCdBgSGyq7HOoyqWu9kR1FdbBYOW6EiK6MYYS81vauKb2TBkVxCXgPMnqAAaE6DRrbO3G0ggsWEtGVMYyQ17KvZcFVVz2LRq1Cdppt64ftp7gaKxFdGcMIeaVWoxn55Q0AgEmDOF7E09i7arZx8TMi6gWGEfJKu0rqYLYKJEcGITkyWHY59D321qrdxXUwmblDNxFdHsMIeSX7eJHJbBXxSEPjwhAVokV7p8XRgkVE1BOGEfJK9vEiORwv4pFUKsVxbThuhIiuhGGEvE59qwlHK22zNDhexHPZr832Qo4bIaLLYxghr5NXVAshgIy4UMSE6WSXQz2YPNjWMrK/vB5tJrPkaojIkzGMkNexN/uzVcSzDYwMxoDwIHRaBHaX1Msuh4g8GMMIeR17sz/XF/FsiqI4rpF9wDER0aUwjJBXqWxsR1FNK1QKkJ3OMOLpJnetN7Kd640Q0WUwjJBXsbeKjEoKhyEoQHI1dCX2GTWHKxrR0GaSXA0ReSqGEfIqXALeu8TpAzE4NhRC2DbOIyK6FIYR8hpCCMfgVS525j0mcb0RIroChhHyGiW1bahs7IBWrcK1KRGyy6Fecqw3wnEjRNQDhhHyGtu6ZmSMTQlHkFYtuRrqrYnpkVAUoPBcC842dcguh4g8EMMIeY08x3gRdtF4k/BgLUYmGgCcv4ZERBdiGCGvYLVeMF5kMAeveptJXddsG9cbIaJLYBghr3C8qhn1bZ0I0aoxOilcdjnkpAvHjQghJFdDRJ6GYYS8gr1VZEJaJALUfNl6m/GpEQhQKzjT0I6yujbZ5RCRh+FfdfIK2zlexKsFazXISrbNgOKsGiL6PoYR8nhmixW7im0LZuVwsTOvZb92HMRKRN/HMEIe79CZRrQYzTAEBWB4gl52OdRHOY7FzzhuhIi6Yxghj5dXZPskPTE9EiqVIrka6qusgeHQaVSoaTHiVHWL7HKIyIMwjJDHszfr53CXXq+m06gxLpXjRojoYgwj5NFMZit2l9jGi0wazMGr3s4+AJnjRojoQgwj5NHyyxvQ0WlFdKgWQ2JDZZdDV2liV+tWXlEtrFaOGyEiG4YR8mj2T9AT06OgKBwv4u1GJxkQolWjoa0Tx6uaZZdDRB6CYYQ8mn2xM07p9Q0BahXGp0UCOH9tiYgYRshjdXRasL+sAQAXO/Mlk7qC5Y4ijhshIhuGEfJYe0vrYbJYEa8PRGpUsOxyyEVy0m3BcmdRHcwWq+RqiMgTMIyQx8pzLAHP8SK+ZHiiHvpADZqNZhypaJJdDhF5AIYR8lj2MQUTOV7Ep6hVCrLTz6/GSkTEMEIeqcVoxsHTjQDOjzEg32G/pnkcN0JEYBghD7W7pA5mq0ByZBCSIjhexNfYZ0ftLq6DycxxI0T+jmGEPNIO+3iRdM6i8UUZsWGICtGivdOCg6cbZJdDRJIxjJBHso8l4PoivkmlUhyrsXLcCBExjJDHaWzrxJEK23gRhhHfZb+23KeGiBhGyOPsLK6FVQDpMSGI0wfKLofcxB5G9pbVo6PTIrkaIpKJYYQ8jn2GRU46W0V8WXp0CGLDdDCZrdhXVi+7HCKSiGGEPM75xc44eNWXKYpyfoovu2qI/BrDCHmU2hajYzfXiemRkqshd7N31XAQK5F/Yxghj7KjqA4AMDQuDFGhOsnVkLvZW78OlDeg1WiWXA0RycIwQh7FvgT8pMEcL+IPkiODkRQRBLNVYHdJnexyiEgShhHyKPbBqxwv4j+4NDwRMYyQx6hq7EBRdStUCjAhjeNF/IU9eHIQK5H/Yhghj5FXZOuiGTXAAENQgORqqL/YB7EePtOIxrZOydUQkQwMI+Qxthfal4BnF40/idMHYlBMCKzCtuAdEfkfhhHyCEIIx/TOSVwC3u/Yu2o4xZfIPzGMkEcor2vHmYZ2BKgVjEuNkF0O9TMufkbk3xhGyCPYp/RmJUcgWKuRXA31N/sOvifONqO62Si5GiLqbwwj5BHszfPcpdc/RYRoMTxBDwDYwSm+RH6HYYSk43gRAs5fe44bIfI/DCMkXeG5FtS0GKHTqDBmYLjsckiSHMe4kRrJlRBRf2MYIensn4THp0ZCp1FLroZkmZAWCbVKQUltG840tMsuh4j6EcMISWcfvMrxIv4tLDAAowYYAHBWDZG/YRghqSxW4dipl+NF6Py4EXbVEPkThhGS6lhlExrbOxGq0zg+FZP/unCfGiGE5GqIqL8wjJBU9k/A2WmR0Kj5cvR316ZEQKtWobKxAyW1bbLLIaJ+wr/+JBXXF6ELBWnVyOqaUcWuGiL/wTBC0nRarNhVbB8vws3xyIb71BD5H4YRkubg6Qa0mSyICA7AsPgw2eWQh5g02NZKtuNULaxWjhsh8gcMIyTN9sLzXTQqlSK5GvIUmUnhCApQo7bVhJPnmmWXQ0T9gGGEpDk/XoRdNHSeVqPC+LRIAMC2QnbVEPkDhhGSot1kwd7SegBATjoHr1J3k7g0PJFfcTqM5ObmYt68eUhMTISiKFi3bl2vH7tt2zZoNBqMGTPG2aclH7OntA4mixUJhkAMigmRXQ55mCmDba1lO4rq0GmxSq6GiNzN6TDS2tqKzMxMrFixwqnHNTQ0YMGCBZg5c6azT0k+aGuh7RPv5MHRUBSOF6HuhifoER4cgBajGQdPN8guh4jcTOPsA+bMmYM5c+Y4/UQLFy7EvffeC7Va7VRrCvmmbV1hxP4JmOhCKpWCyYOi8fmhSmwtqMW1KZGySyIiN+qXMSNvvfUWioqKsHTp0l4dbzQa0dTU1O1GvqO+1YQjFbZrap/GSfR9k7uCqj24EpHvcnsYKSgowLPPPot3330XGk3vGmKWL18Og8HguCUnJ7u5SupPeUW1EAIYGheG2LBA2eWQh5rcFVT3l9ej1WiWXA0RuZNbw4jFYsG9996LZcuWISMjo9ePW7x4MRobGx238vJyN1ZJ/e3C8SJEPRkYGYykiCB0WgR2ldTJLoeI3MjpMSPOaG5uxp49e7B//3488cQTAACr1QohBDQaDTZs2IDrr7/+osfpdDrodDp3lkYSOcaLDGEXDfVMURRMGRyND3aXY1tBDWYMjZVdEhG5iVvDiF6vx6FDh7rd9+c//xnffPMNPvroI6Slpbnz6ckDlde1obS2DRqVgglpDCN0eZO7wshWjhsh8mlOh5GWlhYUFhY6vi4uLkZ+fj4iIyMxcOBALF68GGfOnME777wDlUqFkSNHdnt8bGwsAgMDL7qf/IO9VWRMcjhCdW7NwuQD7IufHa9qRnWzETFhbDEl8kVOjxnZs2cPsrKykJWVBQBYtGgRsrKysGTJEgBAZWUlysrKXFsl+QyOFyFnRIXqMDxBDwDYztVYiXyWIoTw+G0xm5qaYDAY0NjYCL1eL7sc6iOrVWDcb79GXasJHy7MwfhUrh1BV/a7L47h9dwizB+XhBd/mCm7HCJyQm/fv7k3DfWbY1VNqGs1IUSrxpjkcNnlkJewt6JtLaiBF3x2IqI+YBihfmMfL5KdHoUANV961DvjUyMQoFZQ0diBkto22eUQkRvwHYH6jX07eI4XIWcEazUYOzACAFdjJfJVDCPUL4xmC3YV2xau4n405KwpXBqeyKcxjFC/2F/WgPZOC6JDdciIC5VdDnmZyUNsYWT7qVpYrBw3QuRrGEaoX5zfpTcKiqJIroa8zegBBoTpNGhs78SRikbZ5RCRizGMUL/g+iJ0NTRqFSZ2LYDG1ViJfA/DCLldU0cnDpQ3AGAYob7juBEi38UwQm6341QtrAJIjw5BYniQ7HLIS9mD7O6SenR0WiRXQ0SuxDBCbvddAaFR7lsAACAASURBVLto6OoNiglBvD4QJrPVMTOLiHwDwwi5XW5BNQBgWkaM5ErImymKgusybIE292S15GqIyJUYRsitSmpaUVrbhgC1gpyuAYhEfXVdV6DdwjBC5FMYRsit7K0i16ZEIESnkVwNebspg6OhUoCCcy2oaGiXXQ4RuQjDCLnVlhP2LppYyZWQLwgP1iKza5NFdtUQ+Q6GEXIbk9mKvCLbfjT2vn6iq3XdEFtXjb3VjYi8H8MIuc2e0jq0mSyICdNheIJedjnkI6YNtYWRrQU1MFuskqshIldgGCG3sQ8ynDokmkvAk8tkJoXDEBSApg4zDpxukF0OEbkAwwi5Te5J2/oinNJLrqRWKZjStXHelpNcjZXIFzCMkFuca+rAscomKAowdQjDCLnWtCGc4kvkSxhGyC1yu1ZdHTXAgMgQreRqyNdM7RoQffB0A+pbTZKrIaKrxTBCbmH/xMouGnKHBEMQhsaFQQjgO26cR+T1GEbI5SxWga1d0y6vYxghN+HS8ES+g2GEXO7QmUbUt3UiLFCDrK4Fqohczb6QXu7JagghJFdDRFeDYYRczv5JdfKgaGjUfImRe4xLjUBggArnmo04XtUsuxwiugp8pyCXs4cR++JURO4QGKBGTrpt80V21RB5N4YRcqnG9k7sL7ctRMXxIuRu3MWXyDcwjJBLbS+sgcUqMCgmBAPCg2SXQz7OHkb2lNSj1WiWXA0R9RXDCLnU+Sm93KWX3C89OgRJEUEwWazY0bUpIxF5H4YRchkhhKPvnrv0Un9QFMXROsJxI0Tei2GEXObk2RZUNHZAq1EhOy1KdjnkJ+wL6317glN8ibwVwwi5zKbjZwEAkwdFIUirllwN+Yspg6OhVatQVteGU9Utssshoj5gGCGX2XTsHABg5jVxkishfxKi02DiIFtL3Nddr0Ei8i4MI+QStS1G7CurBwDMvIaDV6l/zep6zW06dlZyJUTUFwwj5BK2/npgRKIeCQZO6aX+df0wWxjZW1rPXXyJvBDDCLmE/RPpzGFsFaH+lxQRjGHxYbAK4NsT7Koh8jYMI3TVTGarY1olx4uQLPbuwU3HGUaIvA3DCF21ncW1aDVZEBOmw6gBBtnlkJ+yB+HcE9Uwma2SqyEiZzCM0FVzzKIZFguVSpFcDfmrMUnhiA7Votloxu6SOtnlEJETGEboqggh8HXXeJHrOV6EJFKpFMwYansNfs1ZNURehWGErsrJsy04Xd8OrUaFKUO4BDzJZe+q2XTsHFdjJfIiDCN0VS5cdTVYq5FcDfm7qUO4GiuRN2IYoavCVVfJk3A1ViLvxDBCfXbhqqscL0KegquxEnkfhhHqM/uqq8MT9EgM56qr5Bm4GiuR92EYoT6zf/Kcxb1oyINwNVYi78MwQn3CVVfJk82yz6rhaqxEXoFhhPqEq66SJ7u+q7WOq7ESeQeGEeoT+yya64dy1VXyPFyNlci7MIyQ06xWga+OVAE4vzkZkSdRqRTHQFb7a5WIPBfDCDntwOkGVDZ2IESrxnUZMbLLIbqkOSMTAABfHq6C1crVWIk8GcMIOe2LQ5UAbANXAwPUkqshurTJg6MRFqhBdbMRe0rrZZdDRJfBMEJOEULgi0O2Zu+bR8VLroaoZ1qNCjcMt82qsQdoIvJMDCPklENnGnGmoR3BWjWmD+V4EfJsc0fZumrWs6uGyKMxjJBTPu/6hDljWCy7aMjjTRkSjVCdBlVNHdhfzq4aIk/FMEK9JoTAl/Yumq7BgUSeTKdRO1YItncvEpHnYRihXjtS0YSyujYEBqgwYxhn0ZB3uLmrq+bLQ5UQgl01RJ6IYYR6zT4IcMbQWARrNZKrIeqd6zJiEKJVo6KxA/nlDbLLIaJLYBihXrHNorGFkTmj2EVD3iMwQI3ru/aq+fIwu2qIPBHDCPXK8apmlNS2QadROVa2JPIWc7umoX/Brhoij8QwQr1ibxWZlhGDUB27aMi7TMuIRVCAGqfr23HoTKPscojoexhG6IqEEI4pvXNHs4uGvE+QVu3YyZezaog8D8MIXVHBuRYUVbdCq2YXDXmvmx171bCrhsjTMIzQFX1+0NYqcl1GNMICAyRXQ9Q3M4bFIDBAhdLaNhypaJJdDhFdgGGErujLw7YwcjNn0ZAXC9ZqMKNrCwP7a5qIPAPDCF1W4blmnDzbggC1gpld0yOJvJV9WvoXh6rYVUPkQRhG6LI+za8AAEwZHA1DELtoyLtdPywWOo0KxTWtOHyGXTVEnsLpMJKbm4t58+YhMTERiqJg3bp1lz1+zZo1uOGGGxATEwO9Xo+cnBx89dVXfS6Y+o/VKvDxvjMAgNvHJkmuhujqheo0uHGEbc2Rj/edllwNEdk5HUZaW1uRmZmJFStW9Or43Nxc3HDDDfjiiy+wd+9ezJgxA/PmzcP+/fudLpb6187iOpxpaEeYToMbh7OLhnzDD8YOAAB8kn8GJrNVcjVEBABOr141Z84czJkzp9fH//GPf+z29e9+9zt88skn+Oyzz5CVleXs01M/WtP1yXHu6AQEBqglV0PkGlMGRyMmTIfqZiM2nzjnaCkhInn6fcyI1WpFc3MzIiMjezzGaDSiqamp2436V5vJ7Fh19QfXsouGfIdGrcLtWbbWEXbVEHmGfg8jL730ElpaWjB//vwej1m+fDkMBoPjlpyc3I8VEgB8daQKrSYLBkYGY1xKhOxyiFzqB11joL45fg71rSbJ1RBRv4aR999/H8uWLcPq1asRG9vzSp6LFy9GY2Oj41ZeXt6PVRIArOkauHrH2AFQFEVyNUSuNTQ+DCMS9ei0CHx2sEJ2OUR+r9/CyAcffIDHHnsMq1evxqxZsy57rE6ng16v73aj/lPZ2I6thTUAzn+CJPI19tf2x3vZVUMkW7+EkVWrVuHhhx/GqlWrMHfu3P54SroKa/efgRDAhLRIJEcGyy6HyC1uGZMIjUrBgdONKDzXLLscIr/mdBhpaWlBfn4+8vPzAQDFxcXIz89HWVkZAFsXy4IFCxzHv//++1iwYAH+8Ic/IDs7G1VVVaiqqkJjI7fx9kRCCMcnRfsUSCJfFB2qw/ShMQDgWE+HiORwOozs2bMHWVlZjmm5ixYtQlZWFpYsWQIAqKysdAQTAHj99ddhNpvx+OOPIyEhwXF78sknXXQK5EoHTzfiVHUrAgNU3IuGfJ69q2btvjOwWLk8PJEsTq8zMn369Mvu6bBy5cpuX2/evNnZpyCJ7FMdZ4+I5w695POuvyYWhqAAVDV1IO9ULaYMiZZdEpFf4t405GA0W/DpAdvMgjs4cJX8gE6jxrxMWwsg1xwhkodhhBy+PV6NhrZOxOl1mDKYnxDJP9iD9/rDVWgxmiVXQ+SfGEbIwf7J8LasAVCruLYI+Yes5HCkR4egvdOCL7tWHSai/sUwQgCAc00d+Pb4OQBcW4T8i6Ioji0P/rWbCywSycAwQgCA93eVwWwVuDYlAhlxYbLLIepXP7w2CRqVgj2l9ThSwWUHiPobwwjBZLbivZ226dgPTkqVWwyRBHH6QNw00rZ77zvbSyVXQ+R/GEYI649UobrZiJgwHW7idurkpx7qCuLr8s9w8zyifsYwQnhnewkA4N4JA6HV8CVB/unalAgMT9DDaLZi9R6OHSHqT3zn8XOHzzRiT2k9NCoF92UPlF0OkTSKojhaR/65o5QrshL1I4YRP/dOXgkAYM6oBMTqA6XWQiTbLWMSER4cgNP17fima3YZEbkfw4gfq2814ZN824qrD01KkVwNkXyBAWrcNT4ZwPmgTkTuxzDix/61pxxGsxUjEvUYOzBCdjlEHuH+7BQoCvBdQQ0Kz7XILofILzCM+CmLVeCfebYpjA/mpEJRuOIqEQAkRwZj5rA4AMA/80qk1kLkLxhG/NSmY2dxpqEd4cEBuGVMouxyiDyKfSDrR3tPo7mjU24xRH6AYcRPvdPVKnLX+GQEBqglV0PkWSYPjsKgmBC0mixYs++M7HKIfB7DiB8qPNeMrYU1UCm2/nEi6k5RFMdqxG/nlcDKab5EbsUw4ofe2lYCAJh5TRySI4PlFkPkoe4Ym4RQnQZF1a3ILaiWXQ6RT2MY8TOVje34cM9pAMAjk9MkV0PkuUJ1Gsc03//7phBCsHWEyF0YRvzM37YUwWSxYkJqJCamR8ouh8ij/eS6dOg0Kuwtrce2wlrZ5RD5LIYRP3K2qQPv77LtzvvkrCGczkt0BbH6QNwzwbZNwqubTrJ1hMhNGEb8yF+3nILJbMW4lAhMGhQluxwir7Bw2iBo1SrsLqlH3im2jhC5A8OInzjX1IH3d7JVhMhZ8YZA3D3BNnbkj5sKJFdD5JsYRvzE67lFMJqtyBoYjimDo2WXQ+RVfjrd1jqyq7gOO4rYOkLkagwjfqC62Yh3d9oWOXtyJltFiJyVYAjC/PFJAIBXv2brCJGrMYz4gb9/V4SOTisyk8MxLSNGdjlEXumn0wcjQK0gr6gWu4rrZJdD5FMYRnxcTYvRsSHeU2wVIeqzAeFBuHOcbezIq5tOSq6GyLcwjPi4f3xXjPZOC0YnGTB9KFtFiK7Gz6YPgkalYFthLfaUsHWEyFUYRnxYXasJ7+SVAOBYESJXSIoIxg+vtY0d+SPHjhC5DMOID3tpwwm0mSwYOUCP64fFyi6HyCc8PmMwNCoFWwtr8M3xs7LLIfIJDCM+6vCZRqzqWm3113OHs1WEyEWSI4Px6BTbvk7/77OjMJotkisi8n4MIz7IahVY8slhCAHcOiYR2elcbZXIlf5z5hDEhulQUtuGf3xXLLscIq/HMOKD1u4/g31lDQjWqrF4zjWyyyHyOaE6Df6/m22/W3/6phAVDe2SKyLybgwjPqapoxPLvzwOAPj5zCGINwRKrojIN906JhHjUyPQ3mnB7744JrscIq/GMOJjXvu6ADUtRqRHh+CRyWmyyyHyWYqi4LlbRkClAP8+WIntp2pkl0TktRhGfEjB2Was3F4CAFh6ywhoNby8RO40ItGA+7JTAADLPj2KTotVckVE3onvVj5CCIHnPjsCs1XghuFxXPadqJ/8140ZiAgOwImzzY7VjonIOQwjPuLLw1XYVlgLrUaFX88dLrscIr8RHqzFr24aBgB4ZeNJVDcbJVdE5H0YRnxAQ5sJ/++zowCAhdMGYWBUsOSKiPzL/HHJGDXAgGajGc99dgRCCNklEXkVhhEvJ4TAsx8fQlVTB9KiQ/DTaYNkl0Tkd9QqBb+9fSQ0KgWfH6zER3tPyy6JyKswjHi5D3aXY/2RKgSoFbx2dxaCtGrZJRH5pdFJ4fjFDRkAgKWfHkFRdYvkioi8B8OIFys814Jlnx0BADw9eyhGJRkkV0Tk3xZOG4Sc9Ci0mSx48oN8mMycXUPUGwwjXspotuDnq/ajo9OKqUOi8diUdNklEfk9tUrBK3eNQXhwAA6dacRLG07ILonIKzCMeKkX15/A0comRIZo8Yc7M6FScSM8Ik8QbwjEiz8YDQB4PbcIuSerJVdE5PkYRrzQ5hPn8MZW2+Zcv//haMTqueQ7kSe5cUQ87p84EACwaPUB1LRwui/R5TCMeJnqZiN++eEBAMBDk1Ix85o4yRUR0aX8z9zhyIgLRU2LEU9/eABWK6f7EvWEYcSLtJss+PE/96CmxYRh8WF4ds4w2SURUQ8CA9R47Z4saDUqfHuiGi9+xfEjRD1hGPESZosV/7lqH/aXNcAQFIA/3TsWgQGcxkvkyYbF6/G720cBAP665RTe7OpeJaLuGEa8gBACv/7kML4+dg46jQpvPDgOg2NDZZdFRL3ww2uT8PTsoQCA33x+FJ8dqJBcEZHnYRjxAn/8ugCrdpVDpQCv3ZOFcamRsksiIif8bPogPJiTAiGARavzsb2wRnZJRB6FYcTDvb+zDK9uKgAA/Oa2kZg9Il5yRUTkLEVRsGTeCNw8Kh6dFoEf/3MvjlQ0yi6LyGMwjHiwDUeq8D/rDgEAfn79YNyXnSK5IiLqK7VKwcvzx2BieiRajGY89NZulNe1yS6LyCMwjHioDUeq8J+r9sMqgLvGJTv2vCAi7xUYoMbrC8ZhWHwYqpuNuOfvO1B4jnvYEDGMeKB38kqw8N29MJqtuGF4HH57+0goCldYJfIF+sAAvP3IBKREBeN0fTt+8Jft2FVcJ7ssIqkYRjyI1Sqw/MtjWPLJEVgFcM+EZPzlvrHQqHmZiHxJnD4Qa346CWOSw9HY3on7/7GTs2zIr/FdzkMYzRY89a98/G1LEQDglzdm4He3j2IQIfJRUaE6rPrRRMweEQeTxYr/XLUff9tyCkJwpVbyP3yn8wCN7Z148M1d+PRABTQqBX+4MxNPXD+EXTNEPi5Iq8af77sWD01KBQAs//I4fv3JYZgtVrmFEfUzhhHJ9pTU4ZY/bcWOojqE6jR46+Hx+MG1SbLLIqJ+olYpeO6WEfj1fwyHogDv7ijD/L/loaiaA1vJfzCMSGI0W7D8y2O48295KK1tw4DwIKz+SQ6mDomRXRoRSfDolDT85b6xCNNpsK+sAXNe/Q5vbC3mBnvkFxThBR2UTU1NMBgMaGxshF6vl13OVTtS0YhF/zqAE2ebAQA/GJuEpbcMhz4wQHJlRCTbmYZ2PPPRQWztWqV1QlokXvphJgZGBUuujMh5vX3/ZhjpR50WK17PLcIfvz6JTotAVIgWv7tjFFdVJaJuhBB4f1cZfvv5MbSZLAjWqvHMTcNwb/ZABHBQO3kRhhEPYrUKfHawAi9vPInSWtuKi7NHxOG3t49CdKhOcnVE5KnK69rwyw8PYGfXOiQpUcH4+fVDcOuYRM60I6/AMOIBhBDYdOwcXtpwAserbF0y0aE6LJ4zDHeMHcDZMkR0RVarwHs7S/HqpgLUtJgAAOkxIXhy5hD8x+hEqFX8O0Kei2FEIiEEthXW4uWNJ7CvrAEAEBaowcJpg/Dw5FQEazWSKyQib9NmMuOdvFL8bcsp1Ld1AgAy4kLxo6npuHlUAkJ0/LtCnodhRIL6VhM+3nca7+8qQ1F1KwAgMECFhyenYeF1g2AI5gBVIro6LUYzVm4rxuu5RWjqMAMAgrVqzB2VgB9em4QJaZFsdSWPwTDST4QQ2FNaj/d3luHzQ5UwmW2LFQVr1bjz2iQ8PmMwYvWBkqskIl/T2N6Jd3eU4sM95SipPb/778DIYPxgbBJmXhOL4Ql6qNiNQxIxjLiRxSqwp6QOG46exYajVSiva3d8b3iCHvdmD8StYxIRxqm6RORmQgjsLa3Hh3tO4/NDlWgxmh3fiwrRYsqQaEwdEoOpQ6IRxw9G1M/cFkZyc3Px+9//Hnv37kVlZSXWrl2L22677bKP2bx5MxYtWoQjR44gOTkZ//M//4OHHnqo18/pCWGkuaMTO4rqsPFoFb4+dg51rSbH9wIDVLglMxH3ZqcgM8nAJlIikqLNZMZXR6rw+cFK5J2qRavJ0u376dEhGDnAgJED9BiRaMCIRD3Cg7WSqiV/0Nv3b6dHPLW2tiIzMxOPPPII7rjjjiseX1xcjLlz52LhwoV47733sGnTJjz22GNISEjA7NmznX36ftPRacHe0npsP1WD7adqcfB0IywXrIRoCArAzGticePweFyXEc1BqUQkXbBWg9uzknB7VhI6LVbsL2vAdwXVyC2owcHTDSiqaUVRTSs+vWCH4AHhQRgUG4qUyGAMjAzGwCjbf5MjgxHKQbHUT66qm0ZRlCu2jDzzzDP4/PPPcfjwYcd9d999NxoaGrB+/fpePU9/tIzUtZqwr7Qee0rrsa+0HvnlDTB9b7OqgZHBmDE0BrNHxGN8WiQXHyIir9HQZsKB0404fKYRRyoacaSiybHuUU+CtWrEhOkQE6pDdKgOMWE6RIRooQ/UQB8UAH1gAPRBGugDAxCkVSNYq0ZQgBpBWjW0ahVbicl9LSPOysvLw6xZs7rdN3v2bDz11FM9PsZoNMJoNDq+bmpqcktt/z5YgS0nqrG3tB5FNa0XfT/BEIicQVHISY9CzqAoJEVwOWYi8k7hwVpMy4jBtIzz+181tnfiWGUTSmtbUVbXhtLaNpTV2W4NbZ1oM1lQWtt2xdByKWqVgkCNClqNCgFq23+1GhW0atvXapWCALUCtUqBRmX7Wq1SoFIUqBSc/3+V7WuVokCB7UOwSgEUBbDd0/X/CgAosOcfeww6/7XS7esLj/k+d4UoT89mPxibhJEDDFKe2+1hpKqqCnFxcd3ui4uLQ1NTE9rb2xEUFHTRY5YvX45ly5a5uzT8+0Al1h+pcnw9ODYU41IiMDYlAuNTI5EaFcxkT0Q+yxAUgInpUZiYHnXR91qMZtQ0G1HdYnT891yTEQ3tJjS1m9HU0YnmDjOa2jvR1GELLh2dFnRabI3tFqtAq8ly0bgV8lxZAyN8N4z0xeLFi7Fo0SLH101NTUhOTnb589wyJhHpMSEYlxqBsQMjOJCLiKhLqE6DUJ0GqdEhTj2u02JFe6cF7V3hxGS2wmi2otNihclshclihdkiYLYKmC1WmK0CFqtAp8UKqxCwCluQsQoBq1XAImwzhoQABGzft3Z9bXf++3DcLyAu+H/Hgecf00P9zgxcED3+FO80JDZU2nO7PYzEx8fj7Nmz3e47e/Ys9Hr9JVtFAECn00Gnc/+eLTePSsDNoxLc/jxERP4ioKsbhruQkzPcPgIzJycHmzZt6nbfxo0bkZOT4+6nJiIiIi/gdBhpaWlBfn4+8vPzAdim7ubn56OsrAyArYtlwYIFjuMXLlyIoqIi/OpXv8Lx48fx5z//GatXr8YvfvELF50CEREReTOnw8iePXuQlZWFrKwsAMCiRYuQlZWFJUuWAAAqKysdwQQA0tLS8Pnnn2Pjxo3IzMzEH/7wB/zjH//w6DVGiIiIqP9wOXgiIiJyi96+f3PVLiIiIpKKYYSIiIikYhghIiIiqRhGiIiISCqGESIiIpKKYYSIiIikYhghIiIiqRhGiIiISCqGESIiIpLK7bv2uoJ9kdimpibJlRAREVFv2d+3r7TYu1eEkebmZgBAcnKy5EqIiIjIWc3NzTAYDD1+3yv2prFaraioqEBYWBgURXHZz21qakJycjLKy8t9ds8bXz9Hnp/38/Vz9PXzA3z/HHl+fSeEQHNzMxITE6FS9TwyxCtaRlQqFZKSktz28/V6vU++wC7k6+fI8/N+vn6Ovn5+gO+fI8+vby7XImLHAaxEREQkFcMIERERSaV+7rnnnpNdhExqtRrTp0+HRuMVPVZ94uvnyPPzfr5+jr5+foDvnyPPz728YgArERER+S520xAREZFUDCNEREQkFcMIERERScUwQkRERFL5XBhZsWIFUlNTERgYiOzsbOzateuyx3/44YcYNmwYAgMDMWrUKHzxxRfdvi+EwJIlS5CQkICgoCDMmjULBQUF7jyFy3Lm/P7+979j6tSpiIiIQEREBGbNmnXR8Q899BAURel2u+mmm9x9GpflzDmuXLnyovoDAwO7HePN13D69OkXnZ+iKJg7d67jGE+6hrm5uZg3bx4SExOhKArWrVt3xcds3rwZY8eOhU6nw+DBg7Fy5cqLjnH299pdnD2/NWvW4IYbbkBMTAz0ej1ycnLw1VdfdTvmueeeu+j6DRs2zJ2ncVnOnuPmzZsv+Rqtqqrqdpy3XsNL/X4pioIRI0Y4jvGka7h8+XKMHz8eYWFhiI2NxW233YYTJ05c8XGy3wt9Koz861//wqJFi7B06VLs27cPmZmZmD17Ns6dO3fJ47dv34577rkHjz76KPbv34/bbrsNt912Gw4fPuw45sUXX8Rrr72Gv/71r9i5cydCQkIwe/ZsdHR09NdpOTh7fps3b8Y999yDb7/9Fnl5eUhOTsaNN96IM2fOdDvupptuQmVlpeO2atWq/jidS3L2HAHbqoEX1l9aWtrt+958DdesWdPt3A4fPgy1Wo0777yz23Gecg1bW1uRmZmJFStW9Or44uJizJ07FzNmzEB+fj6eeuopPPbYY93esPvymnAXZ88vNzcXN9xwA7744gvs3bsXM2bMwLx587B///5ux40YMaLb9du6das7yu8VZ8/R7sSJE93OITY21vE9b76Gr776arfzKi8vR2Rk5EW/g55yDbds2YLHH38cO3bswMaNG9HZ2Ykbb7wRra2tPT7GI94LhQ+ZMGGCePzxxx1fWywWkZiYKJYvX37J4+fPny/mzp3b7b7s7Gzxk5/8RAghhNVqFfHx8eL3v/+94/sNDQ1Cp9OJVatWueEMLs/Z8/s+s9kswsLCxNtvv+2478EHHxS33nqry2vtK2fP8a233hIGg6HHn+dr1/CVV14RYWFhoqWlxXGfp11DOwBi7dq1lz3mV7/6lRgxYkS3++666y4xe/Zsx9dX+2/mLr05v0sZPny4WLZsmePrpUuXiszMTFeW5jK9Ocdvv/1WABD19fU9HuNL13Dt2rVCURRRUlLiuM+Tr+G5c+cEALFly5Yej/GE90KfaRkxmUzYu3cvZs2a5bhPpVJh1qxZyMvLu+Rj8vLyuh0PALNnz3YcX1xcjKqqqm7HGAwGZGdn9/gz3aUv5/d9bW1t6OzsRGRkZLf7N2/ejNjYWAwdOhQ//elPUVtb69Lae6uv59jS0oKUlBQkJyfj1ltvxZEjRxzf87Vr+MYbb+Duu+9GSEhIt/s95Ro660q/g674N/MkVqsVzc3NF/0OFhQUIDExEenp6bjvvvtQVlYmqcK+GzNmDBISEnDDDTdg27Ztjvt97Rq+8cYbmDVrFlJSUrrd76nXsLGxEQAues1dyBPeC30mjNTU1MBisSAuLq7b/XFxcRf1XdpVVVVd9nj7f535me7Sl/P7vmeeeQaJiYndXlA33XQT3nnnHWzatAkvvPACtmzZgjlz5sBisbi0/t7oyzkOHToUb775Jj755BO8++67sFqtmDRpEk6fPg3At67hrl27cPjwvqFsuAAABgJJREFUYTz22GPd7veka+isnn4Hm5qa0N7e7pLXvSd56aWX0NLSgvnz5zvuy87OxsqVK7F+/Xr85S9/QXFxMaZOnYrm5maJlfZeQkIC/vrXv+Ljjz/Gxx9/jOTkZEyfPh379u0D4Jq/XZ6ioqICX3755UW/g556Da1WK5566ilMnjwZI0eO7PE4T3gv9M11bekizz//PD744ANs3ry52wDPu+++2/H/o0aNwujRozFo0CBs3rwZM2fOlFGqU3JycpCTk+P4etKkSbjmmmvwt7/9Db/5zW8kVuZ6b7zxBkaNGoUJEyZ0u9/br6G/eP/997Fs2TJ88skn3cZTzJkzx/H/o0ePRnZ2NlJSUrB69Wo8+uijMkp1ytChQzF06FDH15MmTcKpU6fwyiuv4J///KfEylzv7bffRnh4OG677bZu93vqNXz88cdx+PBhqWOQestnWkaio6OhVqtx9uzZbvefPXsW8fHxl3xMfHz8ZY+3/9eZn+kufTk/u5deegnPP/88NmzYgNGjR1/22PT0dERHR6OwsPCqa3bW1ZyjXUBAALKyshz1+8o1bG1txQcffNCrP2wyr6Gzevod1Ov1CAoKcslrwhN88MEHeOyxx7B69eqLmsO/Lzw8HBkZGV5x/XoyYcIER/2+cg2FEHjzzTfxwAMPQKvVXvZYT7iGTzzxBP7973/j22+/RVJS0mWP9YT3Qp8JI1qtFtdeey02bdrkuM9qtWLTpk3dPjlfKCcnp9vxALBx40bH8WlpaYiPj+92TFNTE3bu3Nnjz3SXvpwfYBsB/Zvf/Abr16/HuHHjrvg8p0+fRm1tLRISElxStzP6eo4XslgsOHTokKN+X7iGgG3andFoxP3333/F55F5DZ11pd9BV7wmZFu1ahUefvhhrFq1qtuU7J60tLTg1KlTXnH9epKfn++o3xeuIWCbpVJYWNirDwQyr6EQAk888QTWrl2Lb775BmlpaVd8jEe8F7pkGKyH+OCDD4ROpxMrV64UR48eFT/+8Y9FeHi4qKqqEkII8cADD4hnn33Wcfy2bduERqMRL730kjh27JhYunSpCAgIEIcOHXIc8/zzz4vw8HDxySefiIMHD4pbb71VpKWlifb2do8/v+eff15otVrx0UcficrKSsetublZCCFEc3Oz+OUvfyny8vJEcXGx+Prrr8XYsWPFkCFDREdHR7+fX1/OcdmyZeKrr74Sp06dEnv37hV33323CAwMFEeOHHEc483X0G7KlCnirrvuuuh+T7uGzc3NYv/+/WL//v0CgHj55ZfF/v37RWlpqRBCiGeffVY88MADjuOLiopEcHCwePrpp8WxY8fEihUrhFqtFuvXr3ccc6V/M08+v/fee09oNBqxYsWKbr+DDQ0NjmP+67/+S2zevFkUFxeLbdu2iVmzZono6Ghx7ty5fj8/IZw/x1deeUWsW7dOFBQUiEOHDoknn3xSqFQq8fXXXzuO8eZraHf//feL7OzsS/5MT7qGP/3pT4XBYBCbN2/u9ppra2tzHOOJ74U+FUaEEOL//u//xMCBA4VWqxUTJkwQO3bscHxv2rRp4sEHH+x2/OrVq0VGRobQarVixIgR4vPPP+/2favVKn7961+LuLg4odPpxMyZM8WJEyf641QuyZnzS0lJEQAuui1dulQIIURbW5u48cYbRUxMjAgICBApKSniRz/6kZQ/EBdy5hyfeuopx7FxcXHi5ptvFvv27ev287z5GgohxPHjxwUAsWHDhot+lqddQ/s0z+/f7Of04IMPimnTpl30mDFjxgitVivS09PFW2+9ddHPvdy/WX9y9vymTZt22eOFsE1lTkhIEFqtVgwYMEDcddddorCwsH9P7ALOnuMLL7wgBg0aJAIDA0VkZKSYPn26+Oabby76ud56DYWwTWMNCgoSr7/++iV/piddw0udG4Buv1ee+F6odBVPREREJIXPjBkhIiIi78QwQkRERP9/u3UsAAAAADDI33oYe4qilYwAACsZAQBWMgIArGQEAFjJCACwkhEAYCUjAMBKRgCAlYwAACsZAQBWAfdubYzACumwAAAAAElFTkSuQmCC",
            "text/plain": [
              "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1-element Vector{PyCall.PyObject}:\n",
              " PyObject <matplotlib.lines.Line2D object at 0x7fbf2c52a710>"
            ]
          },
          "metadata": {},
          "execution_count": 51
        }
      ],
      "source": [
        "diffusion_1D_theta(81;theta=1/2, sigma=1.2) # C-N method"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TMosKXKMC933",
        "outputId": "c2480453-361e-4ea4-a1ee-be003c275516"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "10×10 SparseMatrixCSC{Float64, Int64} with 26 stored entries:\n",
              "  1.0    ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅ \n",
              " -0.2   1.4  -0.2    ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅ \n",
              "   ⋅   -0.2   1.4  -0.2    ⋅     ⋅     ⋅     ⋅     ⋅     ⋅ \n",
              "   ⋅     ⋅   -0.2   1.4  -0.2    ⋅     ⋅     ⋅     ⋅     ⋅ \n",
              "   ⋅     ⋅     ⋅   -0.2   1.4  -0.2    ⋅     ⋅     ⋅     ⋅ \n",
              "   ⋅     ⋅     ⋅     ⋅   -0.2   1.4  -0.2    ⋅     ⋅     ⋅ \n",
              "   ⋅     ⋅     ⋅     ⋅     ⋅   -0.2   1.4  -0.2    ⋅     ⋅ \n",
              "   ⋅     ⋅     ⋅     ⋅     ⋅     ⋅   -0.2   1.4  -0.2    ⋅ \n",
              "   ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅   -0.2   1.4  -0.2\n",
              "   ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅    1.0"
            ]
          },
          "metadata": {},
          "execution_count": 52
        }
      ],
      "source": [
        "# ways to build matrix\n",
        "NX = 10\n",
        "theta = 1\n",
        "nu = 0.3\n",
        "dx = 2 / (NX - 1)\n",
        "dt = (0.2*(dx^2))/nu\n",
        "A = diagm(ones(Float64,NX)); # initialize a matrix\n",
        "for row in 2:NX-1 # loop by row\n",
        "    A[row,row-1] = -theta*nu*dt/dx^2\n",
        "    A[row,row] = 2*theta*nu*dt/dx^2 + 1\n",
        "    A[row,row+1] =  -theta*nu*dt/dx^2\n",
        "end\n",
        "sparse(A)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4obDp2mvDfZg",
        "outputId": "ac8cbc15-ef00-46cb-b5e6-f8db3b75fd6b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "10×10 SparseMatrixCSC{Float64, Int64} with 28 stored entries:\n",
              "  1.4  -0.2    ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅ \n",
              " -0.2   1.4  -0.2    ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅ \n",
              "   ⋅   -0.2   1.4  -0.2    ⋅     ⋅     ⋅     ⋅     ⋅     ⋅ \n",
              "   ⋅     ⋅   -0.2   1.4  -0.2    ⋅     ⋅     ⋅     ⋅     ⋅ \n",
              "   ⋅     ⋅     ⋅   -0.2   1.4  -0.2    ⋅     ⋅     ⋅     ⋅ \n",
              "   ⋅     ⋅     ⋅     ⋅   -0.2   1.4  -0.2    ⋅     ⋅     ⋅ \n",
              "   ⋅     ⋅     ⋅     ⋅     ⋅   -0.2   1.4  -0.2    ⋅     ⋅ \n",
              "   ⋅     ⋅     ⋅     ⋅     ⋅     ⋅   -0.2   1.4  -0.2    ⋅ \n",
              "   ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅   -0.2   1.4  -0.2\n",
              "   ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅   -0.2   1.4"
            ]
          },
          "metadata": {},
          "execution_count": 53
        }
      ],
      "source": [
        "# use spdiagm, check https://docs.julialang.org/en/v1/stdlib/SparseArrays/\n",
        "A = spdiagm(0 => fill(2*theta*nu*dt/dx^2+1,NX),\n",
        "          -1 => fill(-theta*nu*dt/dx^2,NX-1),\n",
        "           1 => fill(-theta*nu*dt/dx^2,NX-1))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FYwV8lUNFHCk",
        "outputId": "9ad31fb5-e899-40fe-b890-3e954a29ad14"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "10×10 SparseMatrixCSC{Float64, Int64} with 28 stored entries:\n",
              "  1.0   0.0    ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅ \n",
              " -0.2   1.4  -0.2    ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅ \n",
              "   ⋅   -0.2   1.4  -0.2    ⋅     ⋅     ⋅     ⋅     ⋅     ⋅ \n",
              "   ⋅     ⋅   -0.2   1.4  -0.2    ⋅     ⋅     ⋅     ⋅     ⋅ \n",
              "   ⋅     ⋅     ⋅   -0.2   1.4  -0.2    ⋅     ⋅     ⋅     ⋅ \n",
              "   ⋅     ⋅     ⋅     ⋅   -0.2   1.4  -0.2    ⋅     ⋅     ⋅ \n",
              "   ⋅     ⋅     ⋅     ⋅     ⋅   -0.2   1.4  -0.2    ⋅     ⋅ \n",
              "   ⋅     ⋅     ⋅     ⋅     ⋅     ⋅   -0.2   1.4  -0.2    ⋅ \n",
              "   ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅   -0.2   1.4  -0.2\n",
              "   ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅     ⋅    0.0   1.0"
            ]
          },
          "metadata": {},
          "execution_count": 54
        }
      ],
      "source": [
        "# change the value in 1st and last row\n",
        "A[1,1] = 1\n",
        "A[1,2] = 0\n",
        "A[NX, NX] = 1\n",
        "A[NX, NX-1] = 0\n",
        "A"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "aHSk3B5CF7_9"
      },
      "outputs": [],
      "source": [
        "# Solving Large Sparse Linear Systems\n",
        "# AU = B\n",
        "\n",
        "# U = A \\ B \n",
        "# using LU or QR factorization\n",
        "\n",
        "# when A is large, maybe we need some iterative method, like gmres, cg\n",
        "# check https://nextjournal.com/sosiris-de/pde-2018 for more details\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_C2dTKONHTfp",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "08114501-9c65-4e44-95d8-bc8dae7cf6d7"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "solve_heat (generic function with 1 method)"
            ]
          },
          "metadata": {},
          "execution_count": 58
        }
      ],
      "source": [
        "# # simple Heat Equation\n",
        "# We consider the heat equation on the unit interval, with Dirichlet boundary conditions:\n",
        "# ∂ₜu = Δu\n",
        "# u(x=0,t)  = a\n",
        "# u(x=1,t)  = b\n",
        "# u(x, t=0) = u₀(x)\n",
        "#\n",
        "# For `a = b = 0` and `u₀(x) = sin(2πx)` a solution is given by:\n",
        "# note that `a = b = 0`, so u(x,t) at boundary always equals 0\n",
        "using SparseArrays\n",
        "u_analytic(x, t) = sin(2*π*x) * exp(-t*(2*π)^2)\n",
        "\n",
        "function solve_heat(;theta=1.0, sigma=0.1)\n",
        "    Δx = 0.01\n",
        "    x = Δx:Δx:1-Δx # we dont need the point x=0 and x=1 here\n",
        "    N = length(x)\n",
        "    t0 = 0.0\n",
        "    t1 = 0.03\n",
        "    Δt = sigma*Δx^2\n",
        "    u0 = u_analytic.(x, t0)\n",
        "\n",
        "    A = spdiagm(0=>(1+2*sigma*theta)*ones(N), -1=>-sigma*theta*ones(N-1), 1=>-sigma*theta*ones(N-1))\n",
        "    B = spdiagm(0=>(1-2*sigma*(1-theta))*ones(N), -1=>sigma*(1-theta)*ones(N-1), 1=>sigma*(1-theta)*ones(N-1))\n",
        "\n",
        "    u_next = copy(u0)\n",
        "\n",
        "    for i in Δt:Δt:t1\n",
        "        u_next = A \\ (B*u_next)\n",
        "    end\n",
        "    u_T = u_next\n",
        "\n",
        "    plot(range(Δx, length = N ,stop = 1-Δx),u0,label=\"t=0,numerical\")\n",
        "    plot(range(Δx, length = N ,stop = 1-Δx),u_analytic.(x,t0),\":\",label=\"t=0,analytic\")\n",
        "\n",
        "    plot(range(Δx, length = N ,stop = 1-Δx),u_T,label=\"t=0.03,numerical\")\n",
        "    plot(range(Δx, length = N ,stop = 1-Δx),u_analytic.(x,t1),\":\",label=\"t=0.03,analytic\")\n",
        "    legend()\n",
        "    return u_T\n",
        "end\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "solve_heat(;theta=0, sigma=0.1) #explicit"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 916
        },
        "id": "qgv-f4ibV_Yc",
        "outputId": "d78e94c9-e945-43b9-8b26-bdec753ac325"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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",
            "text/plain": [
              "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "99-element Vector{Float64}:\n",
              "  0.019213390668710875\n",
              "  0.0383509548622156\n",
              "  0.0573371653577638\n",
              "  0.07609709225650405\n",
              "  0.0945566986975624\n",
              "  0.11264313304770798\n",
              "  0.1302850164134666\n",
              "  0.1474127243410035\n",
              "  0.16395866159203412\n",
              "  0.17985752891134837\n",
              "  0.19504658073313838\n",
              "  0.20946587280908138\n",
              "  0.2230584987809014\n",
              "  ⋮\n",
              " -0.20946587280908163\n",
              " -0.19504658073313866\n",
              " -0.17985752891134865\n",
              " -0.16395866159203445\n",
              " -0.14741272434100383\n",
              " -0.13028501641346693\n",
              " -0.11264313304770826\n",
              " -0.09455669869756268\n",
              " -0.07609709225650427\n",
              " -0.05733716535776397\n",
              " -0.038350954862215694\n",
              " -0.01921339066871093"
            ]
          },
          "metadata": {},
          "execution_count": 62
        }
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "name": "julia_diffusion_1D.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Julia",
      "name": "julia"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}
